Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation

DOI10.1134/S0965542516070101zbMath1367.65178OpenAlexW2505520812MaRDI QIDQ519136

Elnur H. Khalilov

Publication date: 4 April 2017

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542516070101

zbMATH Keywords

collocation methodfundamental solutionHelmholtz equationmixed boundary value problemcubature formulasconvergence estimatessurface integral equationproperties of the discretized problem

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (8)

Analysis of approximate solution for a class of systems of integral equations ⋮ Properties of the Operator Generated by the Derivative of the Acoustic Single Layer Potential ⋮ Justification of the collocation method for a class of surface integral equations ⋮ Application of boundary integral equation method to numerical solution of elliptic boundary-value problems in R3 ⋮ Substantiation of the collocation method for one class of systems of integral equations ⋮ Constructive method for solving a boundary value problem with impedance boundary condition for the Helmholtz equation ⋮ Justification of the collocation method for an integral equation of the exterior Dirichlet problem for the Laplace equation ⋮ Approximate solution of the boundary value problem for the Helmholtz equation with impedance condition

Cites Work

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• Regular convergence of operators and approximate solution of equations
• The exterior Dirichlet problem for the Helmholtz equation
• On Neumann's method for the exterior Neumann problem for the Helmholtz equation
• Justification of the collocation method for a class of boundary integral equations
• The exterior Neumann problem for the Helmholtz equation
• Potential-based numerical solution of Dirichlet problems for the Helmholtz equation

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