The parameter-uniform convergence of a fitted operator method on non-uniform meshes for a singularly perturbed initial value problem

TL;DR

This paper proves that a fitted operator method achieves parameter-uniform convergence on non-uniform meshes for singularly perturbed initial value problems, extending previous results limited to uniform meshes.

Contribution

It introduces a new proof technique demonstrating parameter-uniform convergence of the fitted operator method on non-uniform meshes for such problems.

Findings

Parameter-uniform convergence is established on non-uniform meshes.

A novel proof method is developed for this convergence.

The results extend the applicability of fitted operator methods.

Abstract

The parameter-uniform convergence of a fitted operator method for a singularly perturbed differential equation is normally available only for uniform meshes. Here we establish the parameter-uniform convergence of a fitted operator method on a non-uniform mesh for a singularly perturbed initial value problem. This is obtained by a new method of proof.