Numerical convergence of a one step approximation of an intrgro-differential equation

TL;DR

This paper analyzes the numerical stability and convergence of a one-step approximation method for a linear partial integro-differential equation in a periodic domain, relevant to physical and biological modeling.

Contribution

It provides a theoretical analysis of the stability and convergence properties of a specific numerical scheme for integro-differential equations.

Findings

Established conditions for numerical stability.

Proved convergence of the approximation for smooth and non-smooth initial data.

Applicable to modeling in physics and biology.

Abstract

We consider a linear partial integro-differential equation that arises in the modeling of various physical and biological processes. We study the problem in a spatial periodic domain. We analyze numerical stability and numerical convergence of a one step approximation of the problem with smooth and non-smooth initial functions.