Fourier Truncation Regularization Method for a Three-Dimensional Cauchy Problem of the Modified Helmholtz Equation with Perturbed Wave Number

Abstract

In this paper, the Cauchy problem of the modified Helmholtz equation (CPMHE) with perturbed wave number is considered. In the sense of Hadamard, this problem is severely ill-posed. The Fourier truncation regularization method is used to solve this Cauchy problem. Meanwhile, the corresponding error estimate between the exact solution and the regularized solution is obtained. A numerical example is presented to illustrate the validity and effectiveness of our methods.

Keywords

• modified Helmholtz equation
• ill-posed problem
• Cauchy problem
• Fourier truncation method