On the numerical solution of non-linear first order ordinary differential equation systems

TL;DR

This paper introduces a new numerical method for solving non-linear first order ODE systems, demonstrating its application to a flight mechanics boundary value problem with robustness and computational simplicity.

Contribution

The paper develops a difference equation-based numerical method for non-linear first order ODE systems and applies it to a complex boundary value problem in flight mechanics.

Findings

Method is robust and easy to implement computationally.

Successfully applied to a non-linear flight mechanics boundary value problem.

Provides an effective approach for similar differential equation systems.

Abstract

In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a non-linear two point boundary value problem relating a flight mechanics model. We highlight the algorithm obtained seems to be robust and of easy computational implementation.