The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation

摘要

This paper discusses the problem of determining an unknown source whichdepends only on one variable for the modified Helmholtz equation. This problemis 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 simplified Tikhonov regularization method. Convergence estimate is presented between theexact solution and the regularization solution. Moreover, numerical results arepresented to illustrate the accuracy and efficiency of this method.