A discussion on the approximate solutions of first order systems of non-linear ordinary equations

TL;DR

This paper introduces a simple one-step matrix method for approximating solutions to first order non-linear ordinary differential equations, demonstrating convergence and accuracy through various examples.

Contribution

It presents a novel, easy-to-implement matrix method for solving first order systems, with proven convergence and error analysis.

Findings

Method converges to the exact solution

Demonstrated high accuracy on classical examples

Simpler implementation compared to existing methods

Abstract

We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the exact solution. We study the precision, in terms of the local error, of the method by applying it to different well known examples. The advantage of the method over others widely used lies on the simplicity of its implementation.