The finite-difference scheme of higher order of accuracy for the two-dimensional Poisson equation in a rectangle with regard for the effect of the Dirichlet boundary condition

DOI10.1007/s10559-018-0063-7zbMath1404.65217OpenAlexW2884330038MaRDI QIDQ1616265

N. V. Maiko

Publication date: 1 November 2018

Published in: Cybernetics and Systems Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10559-018-0063-7

zbMATH Keywords

boundary effectfinite difference schemePoisson's equationDirichlet boundary conditionerror estimatedifference operatornine-point template

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite difference methods for boundary value problems involving PDEs (65N06)

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Super-exponential rate of convergence of the Cayley transform method for an abstract differential equation ⋮ Weighted Estimates of the Cayley Transform Method for Boundary Value Problems in a Banach Space

Cites Work

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• Boundary effect in the error estimate of the finite-difference scheme for two-dimensional Poisson's equation
• A weighted error estimate for a finite-difference scheme of increased approximation order for a two-dimensional Poisson equation with allowance for the Dirichlet boundary condition
• Weight Uniform Accuracy Estimates of Finite Difference Method for Poisson Equation, Taking into Account Boundary Effect
• Numerical Analysis and Its Applications