Third-Order Improved Runge-Kutta Method for Solving Ordinary Differential Equation

Abstract

In this paper, the fifth order Improved Runge-Kutta method (IRK5) that uses just five function evaluations per step is developed. The method proposed here are derived with only five stages which results in lower number of function evaluations. Therefore, IRK5 has a lower computational cost than the classical fifth order Runge-Kutta method (RK5). Here, the order conditions of the method are obtained up to order six and the coefficients of the f ifth order method are determined by minimizing the error norm of the sixth order method. Numerical examples are given to illustrate the computational efficiency and accuracy of IRK5 in compared with RK5.