... )(ci − c6 )ci = i=1 c6 − , 12 (326b) (326c) (326d) RUNGE–KUTTA METHODS 193 , (326e) , (326f) bi = 1, (326g) bi (1 − ci )ci = i=1 bi ci = i=1 i=1 c3 − , 60 24 (326h) bi (1 − ci )(ci − c6 )aij (cj ... a method derived in this manner: 4 1 8 0 16 −3 7 90 −3 8 16 45 16 − 12 15 16 45 90 192 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS The first methods of this order, derived by Kutta (1901), ... of the matrix A For i corresponding to a member of row k for k = 1, 2, , m, the only non-zero 190 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS aij are for j = and for j corresponding...