Numerical Solver for Initial Value Problems of Ordinary Differential Equations by the IMT-DE Type Numerical Indefinite Integration Formula

Abstract

Abstract. In this paper, we propose a numerical solver for initial value problems of ordinary differential equations using the IMT-DE type numerical indefinite integration formula. In the presented method, we consider the Picard iterative solutions for an integral equation equivalent to the initial value problem and obtain a numerical solution approximating the integral operator appearing in the iterative solutions by the IMT-DE formula. In addition, the iteration is accelerated by the update used in the Gauss-Seidel method for linear systems. A theoretical error analysis and numerical examples show the effectiveness of the presented method.