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An alternating iterative procedure for the Cauchy problem for the Helmholtz equation

Fredrik Berntsson, Vladimir Kozlov, Lydie Mpinganzima, B.O. Turesson

Inverse Problems in Science and Engineering · 2013 · 48 citations · 24 references

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Concepts

Natural SciencesPhysicsComputational PhysicsDifferential EquationsFluid DynamicsFinite Difference MethodsIterative SolversNumerical AlgorithmsNumerical AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsCauchy ProblemConvergenceFinite Difference DiscretizationFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsHelmholtz EquationLipschitz ConditionsNumerical Analysis Of Partial Differential Equations

Abstract

We present a modification of the alternating iterative method, which was introduced by V.A. Kozlov and V. Maz’ya in for solving the Cauchy problem for the Helmholtz equation in a Lipschitz domain. The method is implemented numerically using the finite difference method.