On the difference method for approximation of second order derivatives of a solution of Laplace’s equation in a rectangular parallelepiped

DOI10.2298/FIL1902633DzbMath1499.65610OpenAlexW2996069570WikidataQ126576099 ScholiaQ126576099MaRDI QIDQ5080326

Hediye Sarikaya, Adiguzel A. Dosiyev

Publication date: 31 May 2022

Published in: Filomat (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2298/fil1902633d

zbMATH Keywords

finite difference methoderror estimationsapproximation of derivativesLaplace's equation on parallelepiped

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) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical differentiation (65D25)

Cites Work

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• On a highly accurate approximation of the first and pure second derivatives of the Laplace equation in a rectangular parallelpiped
• On differential properties of solutions of the Laplace and Poisson equations on a parallelepiped and efficient error estimates of the method of nets
• A highly accurate homogeneous scheme for solving the laplace equation on a rectangular parallelepiped with boundary values in C k, 1
• Application of a 14-point averaging operator in the grid method
• On convergence in C2 of a difference solution of the Laplace equation on a rectangle
• On the grid method for approximating the derivatives of the solution of the Dirichlet problem for the Laplace equation on a rectangular parallelepiped

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