Abstract
The Quasi‐Reversibility Regularization Method (Q‐RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace‐type operator in the Helmholtz equation or the imposed Cauchy boundary conditions on the Helmholtz equation. To help bridge this gap in the literature, a Modified Quasi‐reversibility Regularization Method (MQ‐RRM) is introduced to provide additional information in both the Laplace‐type operator occurring in the Helmholtz equation and the imposed Cauchy boundary conditions on the Helmholtz equation, resulting in a strong stable solution and faster convergence of the solution of the Helmholtz equation than the regularized solutions provided by Q‐RRM and its variants methods.
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