Numerical methods for solving second-order initial value problems of ordinary differential equations with Euler and Runge-Kutta fourth-order methods

Abstract

This paper presents two standard numerical methods for solving second order initial value problems for ordinary differential equations (ODEs). The Euler and the Runge-Kutta fourth-order methods are applied without any discretization or restrictive assumptions for solving ODEs. The numerical solutions obtained by the two methods are in good agreement with the exact solutions. The convergence and error analysis which are discussed demonstrate the effectiveness of the methods. The results obtained from the two numerical methods show that the RK4 method is appropriate, consistent, convergent, quite stable, and more accurate than the Euler's method.