A class of Runge–Kutta formulae of order three and four with reduced evaluations of function

Abstract

Traditionally, an explicit Runge–Kutta method of order three requires three evaluations of function and an explicit Runge–Kutta method of order four requires four evaluations of function. In this paper, a class of Runge–Kutta processes of order three and order four with reduced evaluations of function are proposed. The numerical experiments shows that these new Runge–Kutta processes are more attractive than the traditional ones.