§52 Runge-Kuta法 考虑改进 Euler法 Dk=Yx-1+hf(k-L Dk-1 h Dk=Dk+alf(k-lyk1+f(xk Dx) 如果将其改成(1=+2(<1+K2) K,=f(k-1 k-1) (1) K2=f(xk,yk1+hk) yo=y(ro§5.2 Runge-Kutta法 ( , ) k = k -1 + k -1 k -1 y y hf x y [ ( , ) ( , )] 2 k k 1 k 1 k 1 k k f x y f x y h y = y - + - - + 考虑改进Euler法 如果将其改成 ( ) 2 1 K1 K2 h y y k = k - + + ( , ) 1 = k -1 k -1 K f x y ( , ) 2 1 1 K = f xk yk - + hK ( ) 0 0 ï y = y x ï î ï ï í ì ----------(1)