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Modified regularization method for the Cauchy problem of the Helmholtz equation. (English) Zbl 1185.65203

Summary: The Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a modified regularization method to solve it based on the solution given by the method of separation of variables. Convergence estimates are presented under two different \(a-priori\) bounded assumptions for the exact solution. Finally, numerical examples are given to show the effectiveness of the proposed numerical method.

MSC:

65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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