Publications and Software of Ch. Tsitouras

    Edited Volumes

  1. T. E. Simos and Ch. Tsitouras (editors), International Conference in Numerical Analysis and Applied Mathematics (ICNAAM 2004), Wiley-VCH, 2004.
  2. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2005, Wiley-VCH, 2005.
  3. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2006, Wiley-VCH, 2006.
  4. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2007, AIP CP 936, ISBN 978-0-7354-0447-2.
  5. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2008, AIP CP 1048, ISBN: 978-0-7354-0576-9.
  6. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2009, AIP CP 1168, ISBN: 978-0-7354-0705-3.
  7. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2010, AIP CP 1281, ISBN: 978-0-7354-0834-3.
  8. T. E. Simos, G. Psihoyios , Ch. Tsitouras and Z. Anastassi (editors), ICNAAM 2011, AIP Conf. Proc. 1389, ISBN: 978-0-7354-0956-9.
  9. T. E. Simos, G. Psihoyios , Ch. Tsitouras and Z. Anastassi (editors), ICNAAM 2012, AIP Conf. Proc. 1479, ISBN: 978-0-7354-1091-6.
  10. T. E. Simos, G. Psihoyios and Ch. Tsitouras (editors), ICNAAM 2013, AIP Conf. Proc. 1558, ISBN: 978-0-7354-1184-5.
  11. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2014, AIP Conf. Proc. 1648, ISBN: 978-0-7354-1287-3.
  12. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2015, AIP Conf. Proc. 1738, ISBN: 978-0-7354-1392-4
  13. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2016, AIP Conf. Proc. 1863, ISBN: 978-0-7354-1538-6
  14. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2017, AIP Conf. Proc. 1978, ISBN: 978-0-7354-1690-1
  15. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2018, AIP Conf. Proc. 2116, ISBN: 978-0-7354-1854-7
  16. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2019, AIP Conf. Proc. 2293, ISBN: 978-0-7354-4025-8
  17. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2020, AIP Conf. Proc. 2425, ISBN: 978-0-7354-4182-8
  18. T. E. Simos and Ch. Tsitouras (editors), ICNAAM 2021, AIP Conf. Proc. 2849, https://doi.org/10.1063/12.0019668

    Publications in refereed journals

  1. G.Papageorgiou and Ch.Tsitouras, Scaled Runge-Kutta-Nystrom methods for the second order differential equation \(y^{\prime\prime}=f(x,y)\), Int. J. Comput. Math. 28(1988), 139-150.
  2. G. Papageorgiou, Th. Simos and Ch. Tsitouras, Some new Runge-Kutta methods with interpolation properties and their application to the magnetic binary problem, Celestial Mechanics 44(1988), 167-177.
  3. Ch. Tsitouras and G. Papageorgiou, New interpolants for Runge-Kutta algorithms using second derivatives, Int. J. Comput. Math. 31(1989) 105-113.
  4. Ch. Tsitouras and G. Papageorgiou, Runge-Kutta interpolants based on values from two successive integration steps, Computing 43(1990), 255-266.
  5. Ch. Tsitouras, G. Papageorgiou and T. Kalvouridis, Efficiency of Runge-Kutta-Nystrom methods in solving problems of Celestial Mechanics of the form y''=f(x,y,y'), Celestial Mechanics 53(1992), 329-346.
  6. Ch. Tsitouras and G. Papageorgiou, Interpolating Runge-Kutta-Nystrom methods of High order, Int. J. Comput. Math. 47(1992), 209-217.
  7. G. Papageorgiou, Ch. Tsitouras and S. N. Papakostas, Runge-Kutta pairs for periodic initial value problems, Computing 51(1993), 151-163.
  8. S. N. Papakostas, Ch Tsitouras and G. Papageorgiou A new family of efficient 6(5) Runge-Kutta pairs, SIAM J. Numerical Analysis 33(1996), 917-936.
  9. G. Papageorgiou and Ch. Tsitouras, Continuous Runge-Kutta(-Nystrom) methods with reduced Phase-errors, J. Comput. Appl. Math. 69(1996), 1-11.
  10. G. Papageorgiou and Ch. Tsitouras, Interpolation for high order Runge-Kutta methods, Int. J. Comput. Math. 65(1997) 273-291.
  11. S. N. Papakostas and Ch.Tsitouras, Highly Continuous Interpolants for One-Step ODE Solvers and their Application to Runge-Kutta Methods, SIAM J. Num. Anal. 34(1997), 22-47.
  12. Th. Simos and Ch. Tsitouras, A P-stable eighth order method for the numerical integration of periodic initial value problems, J. Comput. Phys., 130(1997), 123-128.
  13. Ch. Tsitouras and Th. Simos, High order explicit methods for the integration of periodic initial value problems Appl. Math. & Comput. 95(1998), 15-26.
  14. Ch. Tsitouras A parameter study of explicit Runge-Kutta pairs of orders 6(5), Appl. Math. Letters 11(1998) 65-69.
  15. G. Papageorgiou, I. Famelis and Ch. Tsitouras A P-stable Diagonally Implicit Runge-Kutta-Nystrom method, Numerical Algorithms 17(1998) 345-353.
  16. Ch. Tsitouras, High order zero-dissipative Runge-Kutta-Nystrom methods, J. Comput. Appl. Math. 95(1998) 157-161.
  17. Ch. Tsitouras, High algebraic order, high dissipation order Runge-Kutta methods, Comput. & Math. w Appl. vol37 i6(1999) 31-36.
  18. Ch. Tsitouras and S. N. Papakostas, Cheap Error Estimation for Runge-Kutta methods, SIAM J. Sci. Comput. 20(1999) 2067-2088. (postscript version 439K)
  19. Ch. Tsitouras, A tenth order symplectic Runge-Kutta-Nystrom method, Celestial Mechanics & Dynamical Astronomy 74(1999) 223-230. (postscript version 93K)
  20. S. N. Papakostas and Ch. Tsitouras, High Phase-Lag Order Runge-Kutta and Nystrom Pairs, SIAM J. Sci. Comput. 21(2000) 747-763. (postscript version 407K)
  21. Ch. Tsitouras, Dissipative high phase-lag order methods, Appl. Math. & Comput. 117(2001) 35-43. (postscript version 100K)
  22. Ch. Tsitouras, Explicit Numerov type methods with reduced number of stages, Comput. & Math. w Appl., 45(2003) 37-42. (postscript version 79K)
  23. Ch. Tsitouras, Optimized explicit Runge-Kutta pair of orders 9(8), Appl. Numer. Math., 38(2001) 123-134. (postscript version 134K)
  24. Ch. Tsitouras and Th. Simos, High order imbedded Numerov-Type methods for the solution of periodic problems, Appl. Math. & Comput., 131(2002) 201-211.
  25. G. Papageorgiou, Ch. Tsitouras and I. Famelis, Explicit Numerov type methods for second order IVPs with oscillating solutions, Int. J. Mod. Phys. C 12(2001) 657-666. (postscript version 118K)
  26. Ch. Tsitouras, Explicit Runge-Kutta pairs appropriate for engineering applications, Appl. Math. Model., 26(2002) 77-88.
  27. Ch. Tsitouras, Runge-Kutta methods for the numerical solution of Initial Value problems, Cubo Matematica Educacional , vol 4, no 2 (2002) 183-199 (pdf versionK).
  28. Ch. Tsitouras, Families of Numerov type methods with high phase-lag order, Appl. Math. & Comput., 135(2003) 169-178.
  29. Ch. Tsitouras, Explicit two step methods for second order linear IVPs, Comput. Math. Appl., 43(2002) 943-949. (pdf version 504K)
  30. Ch. Tsitouras, Neural Networks with multi dimensional transfer functions, IEEE T Neural Networks, 13 (2002) 222-228.(pdf version 181K)
  31. G. Papageorgiou and Ch. Tsitouras, Runge-Kutta pairs for scalar autonomous IVPs, Int. J. Comput. Math., 80(2002) 201-209.(pdf version 106K)
  32. Ch. Tsitouras and Th. Simos, Optimized RK pairs for problems with oscillating solutions J. Comput. Appl. Math. 147(2002) 397-409.(postscript version 142K)
  33. I. Famelis S. N. Papakostas and Ch. Tsitouras, Symbolic derivation of Runge-Kutta order conditions , J. Symbol. Comput. 37(2004) 311-327. (pdf version 167K)
  34. Th. Simos, I. Famelis and Ch. Tsitouras, Zero dissipative, explicit Numerov type methods for second order IVPs with oscillating solutions , Numerical Algorithms 34(2003) 27-40.
  35. P. Psarrakos and Ch. Tsitouras, Numerical Approximation of the boundary of the Numerical Range of Matrix Polynomials, Appl. Numer. Anal. & Comput. Math., 2(2005) 126-133. (pdf version 384K)
  36. A. G. Bratsos, Ch. Tsitouras and D. G. Natsis, Linearized numerical schemes for the Boussinesq equation, Appl. Numer. Anal. & Comput. Math., 2(2005) 34-53.
  37. D. G. Pavlou, N. V. Vlachakis, Ch. Tsitouras, M. G. Pavlou and A. Fatsis, Creep sagging analysis of pressure pipes, Comput. Mater. Sci., 36(2006) 303-309.
  38. Ch. Tsitouras, Stage Reduction on P-Stable Numerov Type Methods of Eighth Order, J. Comput. Appl. Math., 191(2006) 297-305.( pdf version 110K)
  39. A. G. Bratsos, I. Th. Famelis, A. Kollias and Ch. Tsitouras, Phase-Fitted Numerov type methods, Appl. Math. & Comput., 2 (2005) 34-53.
  40. Ch. Tsitouras, Explicit eighth order two-step methods with nine stages for integrating oscillatory problems, Int. J. Modern Phys. C, 17(2006) 861-876. (pdf version 384K)
  41. Ch. Tsitouras and I. Th. Famelis, Symbolic derivation of Runge-Kutta-Nystrom order conditions, J. Math. Chem., 46 (2009) 896-912, (pdf version 199K).
  42. Ch. Tsitouras and I. Th. Famelis, Quadratic SDIRK for chemical reaction problems, MATCH-Commun. Comput. Math. Chem., 60 (2008) 697-710. (pdf version 168K).
  43. G.Pavlou, I. Mavrothanasis, Ch. Tsitouras, S. Avlonitis, V. N. Vlachakis, and M.G. Pavlou, Stress Concentration Analysis of Interfacial Micro-structural Cracks under Internal Singular Loading Sources, J. Comput. Meth. Sci. Engnr., 10 (2010) 3-12.
  44. Ch. Tsitouras, Runge-Kutta interpolants for high precision computations, Numer. Algorithms, 44 (2007) 291-307. (pdf version 200K, coefficients)
  45. I. Th. Famelis and Ch. Tsitouras Symbolic Derivation of Order Conditions for Hybrid Numerov-type methods solving y''=f(x,y), J. Comput. Appl. Math., 218 (2008) 543-555. (pdf version 199K).
  46. Ch. Tsitouras and I. Th. Famelis, Quadratic Stormer-type methods for the solution of the Boussinesq equation by the method of lines, Numer. Meth. PDEs, 24 (2008) 1321-1328.(pdf version 173K).
  47. Ch. Tsitouras,  Rational Approximations to the Solution of the Brusselator System Compared to the Adomian Decomposition Method, Int. J. Contemp. Math. Sci., 4 (2009) 815-820. pdf version
  48. Ch. Massouros and Ch. Tsitouras, Enumeration of hypercompositional structures defined by binary relations, Italian J. Pure & Appl. Maths., 28 (2011) 43-54.(pdf version 109K ).
  49. Ch. Tsitouras and Ch. Massouros, On Enumeration of Hypergroups of Order 3, Comput. Maths. Appl., 59 (2010) 519-523. (pdf version 151K )
  50. Ch. Tsitouras, Rational Approximation to the Abelian Differential Equation Compared to the Abelian Method, Int. J. Comput. Math. & Numer. Simul.., 4 (2011) 45-49.
  51. Ch. Tsitouras, Greatest Remainder Bi-proportional Rounding and the Greek Parliamentary Elections of 2007, Appl. Math. Comput., 217 (2011) 9254-9260. (pdf version 130K)
  52. Ch. Tsitouras, Runge-Kutta pairs of orders 5(4) satisfying only the first column simplifying assumption, Comput. Maths. Appl., 62 (2011) 770-775. (pdf version 139K), (Mathematica code)
  53. Ch. Tsitouras, I. Th. Famelis and T. E. Simos, On modified RK trees and methods, Comput. Maths. Appl., 62 (2011) 2101-2111. (pdf version 236K )
  54. Ch. Tsitouras, Hybrid Hamilton-Webster and the Greek apportionment, Appl. Math. Comput., 218 (2011) 3957-3961. (pdf version 108K, Matlab Implementation)
  55. Ch. Tsitouras and I. Th. Famelis, Using Neural Networks for the derivation of Runge-Kutta-Nystrom pairs for integration of orbits, New Astronomy, 17 (2012) 469-473. (pdf version 135K)
  56. Ch. Tsitouras and C. G. Massouros, Enumeration of Rosenberg type Hypercompositional structures defined by binary relations, Eur. J. Combin., 33 (2012) 1777-1786. (pdf version 179K)
  57. Ch. Tsitouras, On fitted modifications of Runge--Kutta--Nystrom Pairs, Appl. Math. Comput., 232 (2014) 416-423. (pdf version 94K)
  58. Ch. Tsitouras and V. N. Katsikis, Bounds for Variable Degree Rational Loo Approximations to the Matrix Cosine, Comput. Phys. Commun., 185 (2014) 2834-2840.(pdf version 135K)
  59. I. Th. Famelis and Ch. Tsitouras, Quadratic Shooting Solution for a Environmental Parameter Prediction Problem, Far East J. of Appl. Math., 91 (2015), 81.
  60. I. Th. Famelis and Ch. Tsitouras, On modifications of Runge-Kutta-Nystrom methods for solving y''=f(x,y), Appl. Math. Comput., 273 (2016) 726-734.
  61. Ch. Tsitouras, T. E. Simos and I. Th. Famelis, Phase-fitted Runge-Kutta pairs of orders 8(7), J. Comput. Appl. Math., 321 (2017) 226-231.
  62. I. Th. Famelis and Ch. Tsitouras, Symbolic derivation of Runge-Kutta-Nystrom type order conditions and methods for solving y'''=f(x,y), Appl. Math. Comput., 297 (2017) 50-60.
  63. T. E. Simos and Ch. Tsitouras, Evolutionary Generation of High Order Explicit Two Step Methods for Second Order Linear IVPs., Math. Meths Appl. Sci., 40 (2017) 6276-6284.
  64. T. E. Simos, Ch. Tsitouras and I. Th. Famelis, Explicit Numerov type methods with constant coefficients: A Review, Appl. Comput. Math., 16 (2017) 89-113.
  65. I. Th. Famelis, A. Alexandridis, Ch. Tsitouras, High Accuracy Hybrid DE-PSO Algorithm for the construction of Runge Kutta pairs, Enginr. Optim., 50 (2017) 1364-1379.
  66. T. E. Simos and Ch. Tsitouras, A new family of seven stages, eighth order explicit Numerov-type methods, Math. Meths Appl. Sci., 40 (2017) 7867-7878.
  67. D. B. Berg, T. E. Simos and Ch. Tsitouras, Trigonometric fitted, eighth order explicit Numerov-type methods, Math. Meths Appl. Sci., 41 (2018) 1845-1854.
  68. Ch. Tsitouras and I. Th. Famelis, A new eighth order exponentially fitted explicit Numerov-type method for solving oscillatory problems, J. Math. Chem., 56 (2018) 1456-1466.
  69. Ch. Tsitouras and T. E. Simos, On ninth order, explicit Numerov type methods with constant coefficients, Mediterranean J. Maths, 15 (2018) No 46.
  70. T. E. Simos and Ch. Tsitouras, Fitted modifications of classical Runge--Kutta pairs of orders 5(4), Math. Meths Appl. Sci., 41 (2018) 4549-4559.
  71. M. A. Medvedev, T. E. Simos and Ch. Tsitouras, Fitted modifications of Runge--Kutta pairs of orders 6(5), Math. Meths Appl. Sci., 41 (2018) 6184-6194.
  72. Ch. Tsitouras and T. E. Simos, Trigonometric fitted explicit Numerov type method with vanishing phase-lag and its first and second derivatives, Mediterranean J. Maths, 15 (2018) Art. No.:168.
  73. Ch. Tsitouras and I. Th. Famelis, Bounds for Variable Degree Rational Loo Approximations to the Matrix Exponential, Appl. Math. Comput., 338 (2018) 376-386.
  74. M. A. Medvedev, T. E. Simos and Ch. Tsitouras, Explicit, two stage, sixth order, hybrid four--step methods for solving y''=f(x,y), Math. Meths. Appl. Sci., 41 (2018) 6997-7006.
  75. T. E. Simos and Ch. Tsitouras, High phase--lag order, four--step methods for solving y''=f(x,y), Appl. Comput. Math., 17 (2018) 307-316.
  76. M. A. Medvedev, T. E. Simos and Ch. Tsitouras, Trigonometric fitted hybrid four--step methods of sixth order for solving y''=f(x,y), Math. Meths. Appl. Sci., 42 (2019) 710-716.
  77. Chialiang Lin, Jwu Jenq Chen, T. E. Simos and Ch. Tsitouras, Evolutionary derivation of sixth order P--stable SDIRKN methods for the solution of PDEs with the Method of Lines, Mediterranean J. Maths, 16 (2019) 69.
  78. M. A. Medvedev, T. E. Simos and Ch. Tsitouras, Hybrid, phase--fitted, four--step methods of seventh order for solving \(y^{\prime\prime}=f(x,y)\), Math. Meths. Appl. Sci., 42 (2019) 2025-2032.
  79. Jie Fang, Chenglian Liu, Chieh-Wen Hsu, T. E. Simos and Ch. Tsitouras, Explicit hybrid six--step, sixth order, fully symmetric methods for solving y''=f(x,y), Math. Meths. Appl. Sci., 42 (2019) 3305-3314.
  80. C Liu, CW Hsu, TE Simos, C Tsitouras, Phase-fitted, six-step methods for solving \(x^{\prime\prime}=f(t,x)\), Math. Meths. Appl. Sci., 42 (2019) 3942-3949.
  81. Chenglian Liu, Chieh-Wen Hsu, Ch. Tsitouras and T. E. Simos, Hybrid Numerov-Type Methods with Coefficients Trained to Perform Better on Classical Orbits, Bull. Malays. Math. Sci. Soc., 42 (2019) 2119.
  82. Ch. Tsitouras, Explicit Runge--Kutta methods for starting integration of Lane--Emden problem, Appl. Math. Comput., 354 (2019) 353-364.
  83. M. A. Medvedev, T. E. Simos and Ch. Tsitouras, Low-order, P-stable, two-step methods for use with lax accuracies, Math. Meths. Appl. Sci., 42 (2019) 6301-6314.
  84. M. A. Medvedev, T. E. Simos and Ch. Tsitouras, Local interpolants for Numerov-type methods and their implementation in variable step schemes, Math. Meths. Appl. Sci., 42 (2019) 7047-7058. (pdf version)
  85. I. Alolyan, T. E. Simos and Ch. Tsitouras, Interpolants for sixth-order Numerov-type methods, Math. Meths. Appl. Sci., 42 (2019) 7349-7358.
  86. Ch. Tsitouras, Eighth order, phase-fitted, six-step methods for solving \(y^{\prime\prime}=f(x,y)\), J. Math. Chem., 58 (2019) 114-125.
  87. Chialiang Lin, Chieh-Wen Hsu, T. E. Simos and Ch. Tsitouras, Explicit, Semi-Symmetric, Hybrid, Six-Step, Eighth Order Methods for Solving \(y^{\prime\prime}=f(x,y)\), Appl. Comput. Math., 18 (2019) 396-304.
  88. M. A. Medvedeva, T. E. Simos and Ch. Tsitouras, Trigonometric fitted modification of RADAU5, Math. Meths. Appl. Sci., 43 (2020), 1582-1589
  89. M. A. Medvedeva, T. E. Simos and Ch. Tsitouras, Variable step-size implementation of sixth-order Numerov-type methods, Math. Meths. Appl. Sci., 43 (2020) 1204-1215. (html version)
  90. I. Alolyan, T. E. Simos and Ch. Tsitouras, Eighth-order, phase-fitted, four-step methods for solving \(y^{\prime\prime}=f(x,y)\), Math. Meths. Appl. Sci., 43 (2020) 4016-4022.
  91. M. A. Medvedev, T. E. Simos and Ch. Tsitouras, Explicit, Eighth-Order, Four-Step Methods for Solving \(y^{\prime\prime}=f(x,y)\), Bull. Malays. Math. Sci. Soc., 43 (2020) 3791-3807
  92. V. N. Kovalnogov, T. E. Simos and Ch. Tsitouras, Ninth Order, Explicit, Two Step Methods for Second Order Inhomogeneous Linear IVPs, Math. Meths. Appl. Sci., 43 (2020) 4918-4926
  93. T. E. Simos and Ch. Tsitouras, 6th order Runge-Kutta pairs for scalar autonomous IVP, Appl. Comput. Math., 19 (2020) 412-421
  94. T. E. Simos and Ch. Tsitouras, "Explicit, ninth order, two step methods for solving inhomogeneous linear problems \(x^{\prime\prime}=L\cdot x(t)+f(t)\), Appl. Numer. Math., 153 (2020) 344-351
  95. T. E. Simos and Ch. Tsitouras, "Evolutionary derivation of Runge-Kutta pairs for addressing inhomogeneous linear problems", Numer. Algor., 21 (2021) 511-525
  96. M. A. Medvedeva, T. E. Simos Ch. Tsitouras and V. N. Katsikis, Direct estimation of SIR model parameters through second-order finite differences, Math. Meths. Appl. Sci., 44 (2021) 3819-3826. (html version)
  97. M. A. Medvedeva, T. E. Simos and Ch. Tsitouras "Exponential integrators for linear inhomogeneous problems", Math. Meths. Appl. Sci., 44 (2021) 937-944. (html version)
  98. V. N. Kovalnogov, T. E. Simos and Ch. Tsitouras, "Runge-Kutta pairs suited for SIR-type epidemic models", Math. Meths. Appl. Sci., 44 (2021) 5210-5216. (pdf version)
  99. M. A. Medvedeva, T. E. Simos and Ch. Tsitouras "Sixth-order, P-stable, Numerov-type methods for use at moderate accuracies", Math. Meths. Appl. Sci., 44 (2021) 6923-6930
  100. T. E. Simos and Ch. Tsitouras, "Efficiently inaccurate approximation of hyperbolic tangent used as transfer function in artificial neural networks", Neural. Comput. Appl., 33 (2021) 10227-10233
  101. T. E. Simos, Ch. Tsitouras, V. N. Kovalnogov, R. V. Fedorov and D. A. Generalov, "Real time estimation of R0 for COVID-19 spread", Mathematics/MDPI, 9 (2021) 664. (pdf version)
  102. Y-C. Shen, C-L. Lin, T. E. Simos and Ch. Tsitouras, Runge-Kutta Pairs of Orders 6 (5) with Coefficients Trained to Perform Best on Classical Orbits, Mathematics/MDPI, 9 (2021) 1342. (pdf version)
  103. V. N. Kovalnogov, R. V. Fedorov, Y. A. Khakhalev, T. E. Simos and Ch. Tsitouras, A Neural Network Technique for the Derivation of Runge-Kutta Pairs Adjusted for Scalar Autonomous Problems, Mathematics/MDPI, 9 (2021) 1842. (pdf version)
  104. T. E. Simos and Ch. Tsitouras, On high order Runge-Kutta-Nystrom pairs, J. Comput. Appl. Maths., 400 (2022) 113753.
  105. Z. Mingliang, T. E. Simos, Ch. Tsitouras, R0 estimation for COVID-19 pandemic through exponential fit, Math. Meths. Appl. Sci., (2021)  (pdf version). 
  106. V. N. Kovalnogov, R. V. Fedorov, A. V. Chukalin, T. E. Simos and Ch. Tsitouras, Evolutionary derivation of Runge-Kutta pairs of orders 5(4) specially tuned for problems with periodic solutions, Mathematics/MDPI, 9 (2021) 2306. (pdf version)
  107. V. N. Kovalnogov, R. V. Fedorov, T. V. Karpukhina, T. E. Simos and Ch. Tsitouras, Runge-Kutta Pairs of Orders 5(4) Trained to Best Address Keplerian Type Orbits, Mathematics/MDPI, 9 (2021) 2400. (pdf version)
  108. V. N. Kovalnogov, R. V. Fedorov, T. V. Karpukhina, T. E. Simos and Ch. Tsitouras, Sixth Order Numerov-type methods with coefficients trained to perform best on problems with oscillating solutions, Mathematics/MDPI, 9 (2021) 2756. (pdf version)
  109. V. N. Kovalnogov, R. V. Fedorov, A. V. Chukalin, T. E. Simos and Ch. Tsitouras, Eighth Order Two-Step Methods Trained to Perform Better on Keplerian-Type Orbits, Mathematics/MDPI, 9 (2021) 3071. (pdf version)
  110. H. Jerbi, M. Omri, M. Kchaou, T. E. Simos and Ch. Tsitouras, Runge-Kutta-Nystrom Pairs of Orders 8 (6) with Coefficients Trained to Perform Best on Classical Orbits, Mathematics/MDPI, 10 (2022) 654. (pdf version)
  111. H. Jerbi, S. Ben Aoun, M. Omri, T. E. Simos and Ch. Tsitouras, A Neural Network Type Approach for Constructing Runge-Kutta Pairs of Orders Six and Five That Perform Best on Problems with Oscillatory Solutions, Mathematics/MDPI, 10 (2022) 827. (pdf version)
  112. V. N. Kovalnogov, R. V. Fedorov, D. A. Generalov, E. V. Tsvetova, T. E. Simos and Ch. Tsitouras, On a New Family of Runge-Kutta-Nystrom Pairs of Orders 6(4), Mathematics/MDPI, 10 (2022) 875. (pdf version)
  113. V. N. Kovalnogov, M. I. Kornilova, Y. A. Khakhalev, D. A. Generalov, T. E. Simos and Ch. Tsitouras, New family for Runge-Kutta-Nystrom pairs of orders 6(4) with coefficients trained to address oscillatory problems, Math. Meths. Appl. Sci., 45 (2022) 7715-7727.
  114. V. N. Kovalnogov, M. I. Kornilova, Y. A. Khakhalev, D. A. Generalov, T. E. Simos and Ch. Tsitouras, Fitted modifications of Runge-Kutta-Nystrom pairs of orders 7(5) for addressing oscillatory problems, Math. Meths. Appl. Sci., https://doi.org/10.1002/mma.8510
  115. V. N. Kovalnogov, R. V. Fedorov, M. T. Karpukhina, M. I. Kornilova, T. E. Simos and Ch. Tsitouras, Runge-Kutta-Nystrom methods of eighth order for addressing Linear Inhomogeneous problems, J. Comput. Appl. Maths., 419 (2023) 114778. (pdf version)
  116. V. N. Kovalnogov, R. V. Fedorov, T. V. Karpukhina, T. E. Simos, Ch. Tsitouras, Runge-Kutta pairs of orders 8(7) for use in quadruple precision computations, Mathematics/MDPI, 10 (2022) 3247. (pdf version)
  117. V. N. Kovalnogov, M. I. Kornilova, Y. A. Khakhalev, D. A. Generalov, T. E. Simos and Ch. Tsitouras, Runge--Kutta pairs of orders 8(7) with extended stability regions for addressing Linear Inhomogeneous systems, Math. Meths. Appl. Sci., 46 (2023) 4212-4224.
  118. V. N. Kovalnogov, R. V. Fedorov, T. V. Karpukhina, C. Y. Evgenievich, T. E. Simos and Ch. Tsitouras, An Algorithmic approach to Runge--Kutta--Nystrom pairs, TWMS J. Pure Appl. Math., 14 (2023) 3-22.
  119. V. N. Kovalnogov, A. F. Matveev, D. A. Generalov, T. V. Karpukhina, T. E. Simos and Ch. Tsitouras, Runge-Kutta-Nystrom Pairs of Orders 8(6) for Use in Quadruple Precision Computations, Mathematics/MDPI, 11 (2023) 891. (pdf version)
  120. Rong Li, R-L. Lin, T. E. Simos and Ch. Tsitouras, A novel approach on high order Runge-Kutta-Nystrom error estimators, Applied and Computational Mathematics, 22 (2023) 246-258
  121. V. N. Kovalnogov, R. V. Fedorov, T. V. Karpukhina, T. E. Simos, Ch. Tsitouras, Runge-Kutta pairs of orders 9(8) for use in quadruple precision computations, Numerical Algorithms, 95 (2024) 1905-1919.
  122. V. N. Kovalnogov, R. V. Fedorov, T. V. Karpukhina, T. E. Simos, Ch. Tsitouras, On reusing the stages of a rejected Runge-Kutta step, Mathematics/MDPI, 11 (2023) 2589. (pdf version)
  123. V. N. Kovalnogov, R. V. Fedorov, D. A. Demidov, M. A. Malyoshina, T. E. Simos, Ch. Tsitouras, Midway reassignment of Runge-Kutta step length, Math. Meths. Appl. Sci., 46 (2023) 16701-16708.
  124. V. N. Kovalnogov, R. V. Fedorov, T. V. Karpukhina, M. I. Kornilova, T. E. Simos, Ch. Tsitouras, Economical handling of Runge-Kutta-Nystrom step rejection, J. Comput. Appl. Maths, 438 (2306) 115528
  125. H. Alharbi, K. Yadav,R. A. Ramadan, H. Jerbi, T. E. Simos, Ch. Tsitouras, Nine-Stage Runge-Kutta-Nystrom Pairs Sharing Orders Eight and Six, Mathematics/MDPI, 12 (2024) 316. (pdf version)
  126. Yu He, Jianing Yang, T. E. Simos, Ch. Tsitouras, A novel class of Runge-Kutta-Nystrom pairs sharing orders 8(6), AIMS Mathematics, 9 (2024) 4882-4895. (pdf version)
  127. Er-Ping Xiang, Chia-Liang Lin, T. E. Simos, Ch. Tsitouras, Handling effectively the rejected stages in Runge-Kutta pairs implementation, Math. Meths. Appl. Sci., 47 (2024) 10390-10399.
  128. O. Alshammari, S. Ben Aoun, M. Kchaou, T. E. Simos, Ch. Tsitouras, H. Jerbi, Eighth-Order Numerov-Type Methods Using Varying Step Length, Mathematics/MDPI, 12 (2024) 2294. (pdf version)
  129. T. E. Simos, Ch. Tsitouras, Eighth Order, Numerov-Like Schemes with Coefficients Tailored for Superior Performance on Oscillatory Solution Problems, AIMS Mathematics, 9 (2024) : 23368-23383. (pdf version)
  130. H. Jerbi, S. Ben Aoun, O. Alshammari, T. E. Simos, Ch. Tsitouras, M. Kchaou, On explicit ninth order, two-step methods addressing \(y^{\prime\prime}=f(x,y)\), Math. Meths. Appl. Sci., https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.10448

Submitted for publication

    1. R. Abbassia, S. Ben Aounb, M. Kchaoua, T. E. Simos, Ch. Tsitouras, H. Jerbi, On 10th Order Hybrid Numerov-Type Methods.
    2. H. Jerbi, S. Ben Aounb, V. Jeyamani, A. N. Aledaily, T. E. Simos, Ch. Tsitouras, Explicit 10th order, Hybrid Numerov-like methods for addressing problems of the type \(y^{\prime\prime}=\Lambda\cdot y(x)+g(x).\)

    Conference Proceedings

    1. G. Papageorgiou, T. Kalvouridis and Ch. Tsitouras, "Scaled Runge-Kutta methods: The powerful algorithms for the approximate solution of Dynamical problems", 2nd National Congress on Mechanics, Athens, June 29-July 1, 1989. pp99-108.
    2. R. Krikkis, Ch. Tsitouras and G. Kakatsios, "Generalized steady one dimensional flow for real cases", Amer.Soc. Mech. Engin., Conference Proceedings (1991), 1011-1024.
    3. G. Papageorgiou, Ch. Tsitouras and S. N. Papakostas, "5-th and 6-th order Runge-Kutta pairs for initial value problems with periodical solutions", ERMIS conference, Athens 1992, pp487-497.
    4. S. N. Papakostas, Ch. Tsitouras and G. Papageorgiou, "A new family of efficient 6(5) Runge-Kutta pairs", ERMIS conference, Athens 1992, pp515-516.
    5. M. Lambiris, Ch. Tsitouras and K. Evmorfopoulos, "Four-step, Two-stage, Sixth-order P-Stable methods", Proceedings of ICCMSE 2003, World Scientific, pp337-339 (pdf version 77K).
    6. G. Papageorgiou and Ch. Tsitouras, "Runge-Kutta research at NTUA", Proceedings of ICCMSE 2003, World Scientific, pp xx-xx (pdf version 35K).
    7. D. G. Pavlou, Ch. Tsitouras, N. V. Vlachakis, M. G. Pavlou and V. N. Vlachakis, "Non Linear Stress Analysis of Pressure Pipes under Creep conditions", Proceeidings of ICNAAM 2004, Wiley-VCH, pp 307-311.
    8. Psarrakos, P. and Tsitouras Ch., "Numerical Approximation of the boundary of the Numerical Range of Matrix Polynomials", Proceeidings of ICNAAM 2004, Wiley-VCH, pp 318-320.
    9. P. I. Arsenos, C. Demakos, Ch. Tsitouras, D. G. Pavlou and M. G. Pavlou, "Derivation and Optimization of the Material Cost Function for Natural Gas Pipe- Lines", Lecture Series on Computer and Computational Sciences, VSP, pp 41-44.
    10. A. G. Bratsos, I. Th. Famelis and Ch. Tsitouras, "Phase-Fitted Numerov type methods", Lecture Series on Computer and Computational Sciences, VSP, pp 87-90.
    11. Ch. Tsitouras, "Stage Reduction on P-Stable Numerov Type Methods of Eighth Order", Lecture Series on Computer and Computational Sciences, VSP, pp 510-513.
    12. Ch. Tsitouras and I. Th. Famelis, "Quadrature Numerov-type methods for the solution of Boussinesq equation by the method of lines", 17th World IMACS Congress, Paris 2005, paper T2-I-21-0170. (pdf version)
    13. A. G. Bratsos, Ch. Tsitouras and D. G. Natsis, "An extrapolated linearized finite-difference scheme for the numerical solution of the Boussinesq equation", 17th World IMACS Congress, Paris 2005, paper T2-I-21-0170. (pdf version)
    14. Ch. Tsitouras, Ch. Masouros and M. Lambiris, A Mathematica package enumerating Hypergroups of order 3, Proceeidings of ICNAAM 2005, Wiley-VCH
    15. Ch. Tsitouras and I. Th. Famelis, "Phase-Fitted modified Runge-Kutta pairs of orders 6(5)", ICNAAM 2006, Crete, 2006 (pdf version 105K).
    16. Y. G. Petalas, Ch. Tsitouras, G. S. Androulakis and M. N. Vrahatis, "Evolutionary generation of Runge--Kutta pairs", Proceeidings of ICNAAM 2006, pp 433-437 (pdf version 120K)..
    17. V. Katsikis and Ch. Tsitouras, "Computational methods in finite differential lattice subspaces: An application in economics", Proceeidings of ICNAAM 2006, pp 406-410.
    18. Y. G. Petalas, Ch. Tsitouras, G. S. Androulakis and M. N. Vrahatis, "Generating Symmetric Composition Methods through Memetic Algorithms", Lecture Series on Computer and Computational Sciences, VSP 2006 (pdf version 149K).
    19. A. Fatsis, Ch. Tsitouras, A. Panoutsopoulou and N. Vlachakis, "Mathematical Formulation of 3D Non-Reflecting Boundary Conditions for Hyperbolic Equations for Internal Flows in Thermal Engines", AIP CP936 (2007) 199-203.
    20. Ch. Tsitouras, "Greek Electoral System: Optimal Distribution of the Seats", AIP CP936 (2007) 555-557.
    21. Ch. Tsitouras, "Using Neural Networks for the Derivation of Runge-Kutta-Nystrom Pairs", AIP CP1048 (2008) 1034-1036. (pdf version 35K)
    22. Ch. Massouros, Ch. Tsitouras and S. Voliotis, "Square Roots of Total Boolean Matrices", ICSSIP 2009, doi:10.1109/IWSSIP.2009.5367718 (pdf version 220K)
    23. Ch. Tsitouras, "Runge-Kutta pairs of orders 5(4) using the minimal set of simplifying assumptions", AIP CP1168 (2009) 69-72. (pdf version 39K)
      24. version 220K)
    24. Ch. Tsitouras, "Trigonometric fitted Runge-Kutta-Nystrom pair of orders 6(4)", AIP CP1558 (2013) 2509-2511.
    25. I. Th. Famelis and Ch. Tsitouras, "Quadratic RK Shooting solution for a Environmental Parameter Prediction Boundary Value Problem", AIP CP 1618 (2014) 839-842.
    26. Ch. Tsitouras and V. N. Katsikis, "Solving undamped unforced free oscillators by \(L_{\infty}\) approximations to \(\cos\)", AIP CP 1618 (2014) 824-827.
    27. Ch. Tsitouras, "Evolutionary derivation of quadratic symplectic Runge-Kutta-Nystrom methods", AIP CP 1648 (2015) No740002.
    28. A. Alexandridis, I. Th. Famelis and Ch. Tsitouras, "Long-term time-series prediction using radial basis function neural networks", AIP CP 1648 (2015) No740003.
    29. I. Th. Famelis and Ch. Tsitouras, "Differential evolution for the derivation of Runge Kutta pairs", AIP CP 1648 (2015) No740004.
    30. I. Th. Famelis and Ch. Tsitouras, "On the modification of Differential Evolution strategy for the construction of Runge Kutta pairs", MCEEA-15, MATEC Web of Conferences, Volume 41 (2016), https://doi.org/10.1051/matecconf/20164105001. (pdf version)
    31. I. Th. Famelis, S. Tsitmidelis and Ch. Tsitouras, "Evolutionary construction of Runge-Kutta-Nystrom pairs of orders 5(4)", MCEEA-15, MATEC Web of Conferences, Volume 41 (2016), https://doi.org/10.1051/matecconf/20164105002. (pdf version)
    32. S. N. Papakostas, S. Tsitmidelis and C Tsitouras, Evolutionary Generation of 7th order Runge - Kutta - Nystrom Type Methods for Solving y''''=f(x,y), AIP CP 1702 (2016) No 190018.
    33. Ch. Tsitouras and I. Th. Famelis, "Minimax vs Pade Approximation of Matrix Exponential for Normal and Nonnegative Matrices", AIP CP 1702 (2016) No 190013.
    34. V. N. Katsikis, S. N. Papakostas, S. Tsitmidelis and Ch Tsitouras, "Evolutionary generation of explicit two step methods for second order linear IVPs", AIP CP 1738 (2016) No 480038.
    35. I. Th. Famelis, S. Tsitmidelis and Ch. Tsitouras, Evolutionary Generation of high oder Runge - Kutta - Nystrom type pairs for solving y''''=f(x,y),AIP CP 1738 (2016) No 480037.
    36. A. Alexandridis, I. Th. Famelis and Ch. Tsitouras, "Particle Swarm Optimization for Complex Nonlinear Optimization Problems", AIP CP 1738 (2016) No480120.
    37. I. Th. Famelis and Ch. Tsitouras, "High Phase-Lag Order Runge Kutta Pairs of Orders 8(7)", AIP CP 1863 (2017) No560031.
    38. Ch. Tsitouras and I. Th. Famelis, New Phase-fitted Runge-Kutta Pairs of Orders 8(7), AIP CP 1978 (2019) No470005.
    39. Ch. Tsitouras and I. Th. Famelis, Extended precision rational Loo approximations to the matrix exponential, AIP CP 2116 (2019) No450009.
    40. A. Ch. Tsitouras and Ch. Tsitouras, Cubic spline approximation of transfer functions for speeding neural networks performances, AIP CP 2293 (2020) No420015.

    Other work

    1. G.Papageorgiou and Ch.Tsitouras, "Practical Runge-Kutta-Nystrom methods for the equation y''=f(x,y), with interpolation properties", Dept. of Math.,Tech. Rep #1/1987,42pg., NTUA.
    2. Ch. Tsitouras ''Methods for dense output in Runge-Kutta algorithms'', M.Sc. Dissertation, in Greek, University of Athens, 1988.
    3. Ch. Tsitouras ''Continuous extensions of Runge-Kutta type methods for Initial value problems'', Ph.D. dissertation, in Greek, Athens 1990. (pdf version 4.13M)
    4. G. Papageorgiou and Ch. Tsitouras, "High order Runge-Kutta & Runge-Kutta-Nystrom interpolants", Conference on the Solution of ODE's, Helsinki, June 1990.
    5. G. Papageorgiou and Ch. Tsitouras, "Runge-Kutta-Nystrom interpolants with reduced phase Errors", 1st Numerical Analysis Conference, Plovdiv Bulgaria, August 1992.
    6. G. Papageorgiou, Ch. Tsitouras and S. N. Papakostas, "Runge-Kutta pairs for periodic initial value problems", NTUA, Dept. of Math., Tech. Rep. NA 93-1.
    7. Z. Kalogiratou and Ch. Tsitouras, "Intermediate reconsideration of Runge-Kutta step" conference on Scientific Computing and Differential Equations, Grado 1997, B. Owren editor.
    8. Ch. Tsitouras and I. Th. Famelis, "Study and development of Nystrom - type methos for integration of Hamiltonian problems", CHAOS 2013, 11-14 June 2013, Istanbul, Turkey.
    9. Ch. Tsitouras, V. N. Katsikis and I. Th. Famelis, "Rational Loo approximations to the matrix cosine", SCICADE 2013, September 16-20, 2013, Valladolid, Spain.

    1. Mathematica files rktp64.m, rktp75.m, rktp86.m and a Matlab file ode86 for integration of system of ODEs (Journal Paper No18).
    2. Matlab file rkn86 for integration of system of ODEs of second order (Journal Paper No20).
    3. Mathematica file trees16n.m for derivation Runge-Kutta order conditions (Journal Paper No33).
    4. Mathematica file rkn-symbolic.m for symbolic derivation of Runge-Kutta-Nystrom order conditions (Journal Paper No41).
    5. Mathematica file NumericalAlgorithms.txt for the coefficients of the RK9(8) pair and interpolants (Journal Papers No23 & 44).
    6. Mathematica file and Notebook numer.m for two-step Numerov Type methods. (Journal Paper No45).
    7. Mathematica file HyperGroupTest.m for checking HyperGroups (Journal Paper No49).
    8. Mathematica file new54.m producing RK5(4) family pairs (Journal Paper No52).
    9. Supplement file Numerov9sup.pdf for Journal Paper No69.
    10. Mathematica file rkotrees.m, for derivation of order conditions when \(A\cdot e\neq c\). Mathematica file rko5.m, producing 5th order-6 stage methods. Matlab file oliver5.m, for one step of Runge-Kutta-Oliver 6-stages, 5th order (Journal Paper No82).
    11. Matlab file num4.m, implementing 4th order, P-stable, Numerov type method with only 2 stages (Journal Paper No 83)
    12. Matlab file num6v.m, implementing variable step Numerov type method of 6th order (Journal Paper No 89)
    13. Matlab file sir54.m, for integrating SIR-type epidemic models with Runge-Kutta pair (Journal Paper No 98).
    14. Matlab file num6.m,  implementing 6th order, P-stable, Numerov type method with only 4 stages efectively (Journal Paper No 99)
    15. Mathematica file rkn853-liniho.m with the coefficients (Journal Paper No115).
    16. Mathematica file t87.m for derivation of RK pairs orders 8(7) containing the coefficients of T87 pair (Journal Paper No116).
    17. Mathematica file rk87.m for derivation of RK pairs orders 8(7) containing the coefficients of RK87 pair with extended stability region (Journal Paper No117).
    18. Mathematica file rknt86.m Mathematica Implementation of RKNT8(6) pair for use in quadtruple computations (Journal Paper No119).
    19. Mathematica file rkn853.m for derivation of RKN methods of eighth order containing the coefficients of RKN853 triplet (Journal Paper No120).
    20. Mathematica file t98.m for derivation pairs of RK pairs orders 9(8) containing the coefficients of T98 pair. As alternative algorithm see rk98.m (Journal Paper No121).
    21. Mathematica file rknt86q9.m RKN 8(6) with 9 stages, no-FSAL, for quadruple precision computations. (Journal Paper No125).
    22. Mathematica file rknt869.m RKN 8(6) with 9 stages, no-FSAL, for double precision computations. (Journal Paper No126).
    23. Mathematica file rkf45ext.m, RKF5(4) extended pair (Journal paper No127)
    24. Matlab file num8var.m, 8th order Numerov with varying step-length (Journal paper No128)

    Back to the main page.