Polynomial Approximation of an Inverse Cauchy Problem for Modified Helmholtz Equations

Abstract

In this paper, an inverse problem for the modified Helmholtz equation arising in heat conduction in the fin is considered. The goal of this paper is the determination of the temperature at the under-specified boundary (inner boundary of an annular domain) benefiting from the accessible part of the boundary with Cauchy data (boundary temperature and heat flux). This problem is solved numerically using the meshless method proposed in [2]. The stability is confirmed by applying a noise for the Cauchy data.