A sixth‐order improved Runge–Kutta direct method for special third‐order ordinary differential equations

Abstract

In this paper, we construct a four‐stage explicit improved Runge–Kutta direct (IRKD) method of order six for solving special third‐order ordinary differential equations. The sixth‐order IRKD method is a two‐step method and it requires fewer number of stages compared to the classical Runge–Kutta method of the same order per step. The stability properties of the proposed method are given. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method compared with the existing methods in the literature.