Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method

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