A Regularization Method to Solve a Cauchy Problem for the Two-Dimensional Modified Helmholtz Equation

Shangqin He and Xiufang Feng
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Shangqin He: School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China
Xiufang Feng: School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China

Mathematics, 2019, vol. 7, issue 4, 1-13

Abstract: In this paper, the ill-posed problem of the two-dimensional modified Helmholtz equation is investigated in a strip domain. For obtaining a stable numerical approximation solution, a mollification regularization method with the de la Vallée Poussin kernel is proposed. An error estimate between the exact solution and approximation solution is given under suitable choices of the regularization parameter. Two numerical experiments show that our procedure is effective and stable with respect to perturbations in the data.

Keywords: modified Helmholtz equation; ill-posed; de la Vallée Poussin kernel; mollification method; regularization solution; error estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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