(* Runge-Kutta-Nystrom 8(5)3 triplet for linear-inho problems *)
(* from JCAM paper https://doi.org/10.1016/j.cam.2022.114778 *)

a={{0,0,0,0,0,0,0,0},
{3893593/844206654, 0, 0, 0, 0, 0, 0, 0},
{-3399317/288331195,59131649/1139704598,0,0,0,0,0,0},
{170784395/779006567,-415524307/2136417004,137477759/1128017050,0,0,0,0,0},
{-260296467/1014514511,353988425/817226987,-22527982/1056752999,20792035/828316017,0,0,0,0},
{9869956/1117899207,180085946/2025417667,198110639/1117368023,47225497/1319795194,38695631/766210674,0,0,0},
{595786389/685921499,13787663/115494696,-803008540/907075417,583576159/1002451286,-135841514/305934587,165632931/1142331809,0,0},
{27500511/924989552,167938400/1282732299,100567509/597334177,102285865/1211730867,53367357/1030950704,40805111/1204117196,836173/908658872,0}};
c={0,61654500/641946583,15781235/55729866,442273160/816749551,635744090/1058488981,805348954/947366811,1062790099/1209869333,1};
w={27500511/924989552, 167938400/1282732299, 100567509/597334177, 102285865/1211730867, 53367357/1030950704, 40805111/1204117196, 836173/908658872, 0};
w5={306321715/2157974227,0,0,642081431/521967976,-840195381/879805228,69722091/413019176,-72130553/530772928,1/20};
w3={1/3,0,0,0,0,0,0,1/6};
dw={27500511/924989552,110344933/761879290,285171889/1214172202,417193685/2266020388,37227315/287220838,207571215/918218654,7284346/962294909,18694927/432569009};
dw5={-197279247/1553864740,137006885/273488474,-80829197/788832970,95945053/310591416,203827963/891737411,95706644/984051913,477417/943649828,99568687/1068123034};
dw3={215952384/696018025,0,0,0,0,0,2195392932/1406648003,-768631631/882475404};