Numerical Solution for an Inverse Variational Problem

TL;DR

This paper develops a numerical approach to solve an inverse variational problem, proving existence of solutions and demonstrating the effectiveness of the method through numerical examples.

Contribution

It introduces a new numerical method for solving a collage-type inverse variational problem and proves the existence of solutions using a minimax equality.

Findings

Existence of solutions established via minimax equality

Numerical method successfully approximates solutions

Method demonstrated with a numerical example

Abstract

In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve a collage-type inverse problem associated with the corresponding system, and illustrate the behaviour of the method with a numerical example.