Numerical reconstruction of orders in coupled systems of subdiffusion equations

TL;DR

This paper presents a numerical algorithm for simultaneously determining fractional orders in coupled subdiffusion equations, demonstrating its efficiency and accuracy through extensive numerical tests.

Contribution

It introduces a Gauss-Newton iterative method for the inverse problem of identifying fractional orders in coupled subdiffusion systems, based on a reformulation as a minimization problem.

Findings

The algorithm accurately reconstructs fractional orders.

Numerical tests confirm the method's efficiency.

The approach is applicable to coupled subdiffusion systems.

Abstract

In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order inverse problem as a discrete minimization problem, so that we derive a concise Gauss-Newton iterative method. Abundant numerical tests demonstrate the efficiency and accuracy of the proposed algorithm.