On a numerical solution of one nonlocal boundary-value problem with mixed Dirichlet-Neumann conditions

DOI10.1007/s10986-013-9214-8zbMath1327.65200OpenAlexW2076336276MaRDI QIDQ889463

Nodar Khomeriki, Givi Berikelashvili

Publication date: 6 November 2015

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10986-013-9214-8

zbMATH Keywords

convergencefinite difference schemeerror estimatePoisson equationnonlocal boundary value problemintegral constraintsDirichlet and Neumann conditions

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (9)

Radial basis function method for a multidimensional linear elliptic equation with nonlocal boundary conditions ⋮ ALTERNATING DIRECTION IMPLICIT METHOD FOR POISSON EQUATION WITH INTEGRAL CONDITIONS ⋮ Some new operational matrices and its application to fractional order Poisson equations with integral type boundary constrains ⋮ A difference scheme and its error analysis for a Poisson equation with nonlocal boundary conditions ⋮ A matrix formulated algorithm for solving parabolic equations with nonlocal boundary conditions ⋮ Numerical solution of two-dimensional elliptic PDEs with nonlocal boundary conditions ⋮ Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition ⋮ Numerical schemes for general Klein–Gordon equations with Dirichlet and nonlocal boundary conditions ⋮ Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials

Cites Work

• Alternating direction method for the Poisson equation with variable weight coefficients in an integral condition
• Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions
• On a nonlocal generalization of the biharmonic Dirichlet problem
• A fourth-order alternating-direction method for difference schemes with nonlocal condition
• Difference scheme for two-dimensional elliptic problems with an integral condition
• On the convergence of difference schemes for one nonlocal boundary-value problem
• To a nonlocal generalization of the Dirichlet problem
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