Solving the Cauchy problem for an elliptic equation using Bat Algorithm

Abstract

This paper presents a method for solving a class of inverse problems for elliptic equations known as the data completion problem. The goal is to recover missing data on the inaccessible part of the boundary using measurements from the accessible part. The inherent difficulty of this problem arises from its ill-posed nature, as it is susceptible to variations in the input data. To address this challenge, the proposed approach integrates Tikhonov regularization to enhance the stability of the problem. To solve this problem, we use a metaheuristic approach, specifically, the Bat Algorithm (BA) inspired by the echolocation behavior of bats. The performed numerical results show that the Bat Algorithm yields stable, convergent, and accurate solutions.