Nested Runge-Kutta methods for the differential equation y?=F(x, y)

Abstract

Nested Runge-Kutta methods of fourth, fifth, and sixth orders of accuracy are constructed for numerical solution of the Cauchy problem for the ordinary differential equation y”=f(x, y). The first two stages of the fifth- and sixth-order methods determine the fourth-order method, and the ftrst three stages of the sixth-order method determine the fifthorder method. Numerical values of the parameters for these methods are determined and two test problems are solved numerically.