A fourth order accurate approximation of the first and pure second derivatives of the Laplace equation on a rectangle

DOI10.1186/s13662-015-0408-8zbMath1347.65159OpenAlexW2122222061WikidataQ59425037 ScholiaQ59425037MaRDI QIDQ738536

Hamid M. M. Sadeghi, Adiguzel A. Dosiyev

Publication date: 2 September 2016

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-015-0408-8

zbMATH Keywords

Dirichlet problemfinite difference methodnumerical experimentsLaplace equationuniform error boundapproximation of derivatives

Mathematics Subject Classification ID

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

Related Items (8)

A highly accurate difference method for solving the Dirichlet problem for Laplace’s equation on a rectangle ⋮ On the difference method for approximation of second order derivatives of a solution of Laplace’s equation in a rectangular parallelepiped ⋮ Implicit methods for the first derivative of the solution to heat equation ⋮ On a highly accurate approximation of the first and pure second derivatives of the Laplace equation in a rectangular parallelpiped ⋮ A highly accurate difference method for approximating the solution and its first derivatives of the Dirichlet problem for Laplace's equation on a rectangle ⋮ Six Point Implicit Methods for the Approximation of the Derivatives of the Solution of First Type Boundary Value Problem for Heat Equation ⋮ 14-point difference operator for the approximation of the first derivatives of a solution of Laplace’s equation in a rectangular parallelepiped ⋮ On the high order convergence of the difference solution of Laplace’s equation in a rectangular parallelepiped

Cites Work

• The block-grid method for the approximation of the pure second order derivatives for the solution of Laplace's equation on a staircase polygon
• Grid approximation of the first derivatives of the solution to the Dirichlet problem for the Laplace equation on a polygon
• Differentiability properties of solutions of boundary value problem for the Laplace and Poisson equations on a rectangle
• On differential properties of solutions of the Laplace and Poisson equations on a parallelepiped and efficient error estimates of the method of nets
• On convergence in C2 of a difference solution of the Laplace equation on a rectangle
• The High Accurate Block-Grid Method for Solving Laplace's Boundary Value Problem with Singularities
• On the grid method for approximating the derivatives of the solution of the Dirichlet problem for the Laplace equation on a rectangular parallelepiped
• On the solution by the method of grids of the inner Dirichlet problem for the Laplace equation
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