On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions

DOI10.1137/120875570zbMath1295.65103OpenAlexW2025006636MaRDI QIDQ2855117

Dongwoo Sheen, Sean O. Settle, Imbunm Kim, Craig C. Douglas

Publication date: 24 October 2013

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/120875570

zbMATH Keywords

high-order finite difference scheme Helmholtz equation Poisson equation numerical experiment compact scheme Hermitian method

Mathematics Subject Classification ID

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

Related Items (8)

A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients ⋮ Accurate derivatives approximations and applications to some elliptic PDEs using HOC methods ⋮ A sixth order quasi-compact finite difference method for Helmholtz equations with variable wave numbers ⋮ Compact 9-point finite difference methods with high accuracy order and/or M-matrix property for elliptic cross-interface problems ⋮ New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations ⋮ Sixth order compact finite difference schemes for Poisson interface problems with singular sources ⋮ Dirac assisted tree method for 1D heterogeneous Helmholtz equations with arbitrary variable wave numbers ⋮ A new development of sixth order accurate compact scheme for the Helmholtz equation

This page was built for publication: On the Derivation of Highest-Order Compact Finite Difference Schemes for the One- and Two-Dimensional Poisson Equation with Dirichlet Boundary Conditions