(*----------------- Runge-Kutta Tsitouras-Papakostas 7(5) -----------------*)
(*--------------- SIAM J. Sci. Comput., 20 (1999)  2067-2088 --------------*)

a = {{0, 0, 0, 0, 0, 0, 0, 0, 0}, 
     {1/18, 0, 0, 0, 0, 0, 0, 0, 0}, 
     {0, 1/9, 0, 0, 0, 0, 0, 0, 0}, 
     {1/24, 0, 1/8, 0, 0, 0, 0, 0, 0}, 
   {2183971/4000000, 0, -8340813/4000000, 3968421/2000000, 0, 0, 0, 0, 0}, 
   {695768212/7463744411, 0, -1803549175/7007942496, 3474507053/6790877290, 2188198899/15264927763, 0, 0, 0, 0}, 
   {-11894934857/8390623634, 0, 53094780276/9800512003, -8415376229/2277049503, -18647567697/10138317907, 27551494893/11905950217, 0, 0, 0}, 
   {30828057951/7654644085, 0, -4511704/324729, 16217851618/1651177175, 282768186839/40694064384, -104400780537/15869257619, 5409241639/9600177208, 0, 0}, 
   {-133775720546/36753383835, 0, 49608695511/4066590848, -59896475201/7901259813, -48035527651/5727379426, 86266718551/10188951048, -7751618114/23575802495, 2289274942/8464405725, 0}};
 
c = {0, 1/18, 1/9, 1/6, 89/200, 56482/115069, 74/95, 8/9, 1};

bb = {1421940313/46193547077, 0, 0, 1943068601/5911217046, -3807140880/8205366359, 9377220888/11577671635, 586186883/5187186385, 1114095023/8014791121, 1016647712/23899101975}; (* 5th order formula *)

b = {597988726/12374436915, 0, 0, 3138312158/11968408119, 480882843/7850665645, 988558885/3512253271, 5302636961/26425940286, 1259489433/12163586030, 1016647712/23899101975}; (* 7th order formula *)