Identifying an Unknown Source in the Poisson Equation by a Modified Tikhonov Regularization Method

A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation

Inverse Source Identification by the Modified Regularization Method on Poisson Equation

This paper deals with an inverse problem for identifying an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. Since this problem is illposed, we obtain the regularization solution by the modified regularization method. Furthermore, we obtain the Hölder-type error estimate between the regularization s...

A numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems

In this paper‎, two inverse problems of determining an unknown source term in a parabolic‎ equation are considered‎. ‎First‎, ‎the unknown source term is ‎estimated in the form of a combination of Chebyshev functions‎. ‎Then‎, ‎a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem‎. ‎For solving the problem‎, ‎the operational matrices of int...

The Tikhonov Regularization Method in Hilbert Scales for Determining the Unknown Source for the Modified Helmholtz Equation

In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strategy and an a posteriori choice rule have been present to obtain the regularization parameter and corresponding error estimates have been obtained. The smoothness parameter and the a ...

Implementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary ‎condition‎

The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...