Exponentially-fitted forth-order explicit modified Runge-Kutta type method for solving third-order ODEs

Abstract

In this paper exponentially-fitted explicit modified Runge-Kutta type method denoted as EFMRKT for solving y′″(x) = f(x, y, y′) is derived. The idea presented is based on the Simos and Berghe approach which exactly integrates initial value problems whose solutions are linear combinations of the set functions ewx and e−wx with w ∈ R the principal frequency of the problem. We developed the new EFMRKT three-stage fourth-order method called EFRKTG4 for solving third-order initial value problems. The numerical results indicate that EFRKTG4 method is more efficient than existing Runge-Kutta methods.