Identifying an unknown source in the Poisson equation by a wavelet dual least square method

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

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable....

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

Solving a Nonlinear Inverse Problem of Identifying an Unknown Source Term in a Reaction-diffusion Equation by Adomian Decomposition Method

We consider the inverse problem of finding the nonlinear source for nonlinear Reaction-Diffusion equation whenever the initial and boundary condition are given. We investigate the numerical solution of this problem by using Adomian Decomposition Method (ADM). The approach of the proposed method is to approximate unknown coefficients by a nonlinear function whose coefficients are determined from...

The Quasireversibility Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation

This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the quasireversibility regularization method. Convergence estimate is presented between the exact solu...

Landweber iterative regularization method for identifying the unknown source of the time-fractional diffusion equation

In this paper, we investigate an inverse problem to determine an unknown source term that has a separable-variable form in the time-fractional diffusion equation, whereby the data is obtained at a certain time. This problem is ill-posed, and we use the Landweber iterative regularization method to solve this inverse source problem. Two kinds of convergence rates are obtained by using an a priori...