A Novel Approximation on the Solution of Systems of Ordinary Differential Equations

Abstract

In this paper, the initial-value problem for the system of first-order differential equations is considered. To solve this problem, we construct a fitted difference scheme using the finite difference method, which is based on integral identities for the quadrature formula with integral term remainder terms. Next, we prove first-order convergence for the method in the discrete maximum norm. Although this scheme has the same rate of convergence, it has more efficiency and accuracy compared to the classical Euler scheme. Two test problems are solved by using the proposed method and the classical Euler method, which confirm the theoretical findings. The numerical results obtained from here show that the proposed method is reliable, efficient, and accurate.