Numerical Treatment of Non-local Integral Operators in the Framework of Evolutionary Equations

TL;DR

This paper develops a numerical approach for solving abstract differential equations with non-local integral operators within the evolutionary equations framework, proving convergence and demonstrating with simulations.

Contribution

It introduces a new numerical method for non-local integral operators in evolutionary equations and provides convergence analysis and simulations.

Findings

Convergence of the numerical method is proven under specific kernel conditions.

The method effectively approximates solutions to non-local integral equations.

Simulation results validate the theoretical convergence and applicability.

Abstract

Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness of the addressed equation we consider a numerical method of approximating its solution. We provide convergence proofs under conditions on the kernel of the integral operator and the solution and finish the paper with some simulation results.