T - IfB

Order of Runge - Kutta method1 df qpm1m1iki tm1i1 m1m! dt y( t),tup to O(Δt p+1)Example q = p = 1:1 f( yn, tn) f( yn, tn)1 1 gives Euler method.Example q = p = 2:1 df1k12k2 fn t2 dt where index „n“ means „at (y(n ,t n )“.Example q = p = 2n1031 df 1 f f1k12k2 f t f t f2 dt n2 t ny nn n ninsertk1 f( yn, tn) fnk f( y t k , t t )2 n21 1 n2ff fnt21 fnt 2O ty t n 1 1 121, 22 , 2212 2n2( )3 equations for 4 parameters one-parameterfamily104