Galerkin Spectral Method for the Fractional Nonlocal Thermistor Problem

TL;DR

This paper introduces a numerical approach combining backward differentiation and Galerkin spectral methods to solve the time-fractional nonlocal thermistor problem, providing error estimates and demonstrating exponential convergence for smooth solutions.

Contribution

It presents a novel numerical scheme for the fractional thermistor problem with rigorous error analysis and convergence results.

Findings

Error estimates in different contexts are derived.

The method achieves exponential convergence for smooth solutions.

The approach effectively solves the fractional thermistor problem.

Abstract

We develop and analyse a numerical method for the time-fractional nonlocal thermistor problem. By rigorous proofs, some error estimates in different contexts are derived, showing that the combination of the backward differentiation in time and the Galerkin spectral method in space leads, for an enough smooth solution, to an approximation of exponential convergence in space.