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

Fan Yang, Ping Fan and Xiao-Xiao Li
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Fan Yang: School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
Ping Fan: School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
Xiao-Xiao Li: School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China

Mathematics, 2019, vol. 7, issue 8, 1-8

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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