(*----------------- Runge-Kutta Tsitouras-Papakostas 8(6) -----------------*)
(*--------------- SIAM J. Sci. Comput., 20 (1999)  2067-2088 --------------*)
b = {438853193/9881496838, 0, 0, 0, 0, 11093525429/31342013414, 
   481311443/1936695762, -3375294558/10145424253, 9830993862/5116981057, 
   -138630849943/50747474617, 7152278206/5104393345, 5118195927/53798651926};  (* 8th order formula *)
 
bb = {289283091/6008696510, 0, 0, 0, 0, 3034152487/7913336319, 
   7170564158/30263027435, 7206303747/16758195910, -1059739258/8472387467, 
   16534129531/11550853505, -3/2, 5118195927/53798651926};  (* 6th order formula *)
 
a = {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
   {9/142, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
   {178422123/9178574137, 685501333/8224473205, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
   {12257/317988, 0, 12257/105996, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
   {2584949729/6554704252, 0, -9163901916/6184003973, 26222057794/17776421907, 0, 0, 0, 0, 0, 0, 0, 0}, 
   {4418011/96055225, 0, 0, 2947922107/12687381736, 3229973413/17234960414, 0, 0, 0, 0, 0, 0, 0}, 
   {2875139539/47877267651, 0, 0, 2702377211/24084535832, -135707089/4042230341, 299874140/17933325691, 0, 0, 0, 0, 0, 0}, 
   {-7872176137/5003514694, 0, 0, -35136108789/26684798878, -114433184681/9760995895, 299204996517/32851421233, 254/39, 0, 0, 0, 0, 0}, 
   {-3559950777/7399971898, 0, 0, -29299291531/4405504148, -42434013379/9366905709, 20642871700/5300635453, 12951197050/1499985011, 59527523/6331620793, 0, 0, 0, 0}, 
   {-8196723582/10570795981, 0, 0, -46181454005/5775132776, -196277106011/29179424052, 63575135343/11491868333, 120535663067/11060780187, 195434294/9727139945, -617468037/15757346105, 0, 0, 0}, 
   {-6373809055/5357779452, 0, 0, -150772749657/21151088080, -58076657383/6089469394, 9252721190/1221566797, 132381309631/11748965576, 704633904/13813696331, 656417033/8185349658, -1669806516/10555289849, 0, 0}, 
   {-2726346953/6954959789, 0, 0, 24906446731/6359105161, -65277767625/23298960463, 39128152317/16028215273, -40638357893/16804059016, -7437361171/21911114743, 1040125706/5334949109, -1129865134/5812907645, 6253441118/10543852725, 0}};
 
c = {0, 9/142, 24514/238491, 12257/79497, 50/129, 34/73, 23/148, 142/141, 14183175345/16188232343, 83/91, 143/149, 1};