Convergence analysis of the finite difference ADI scheme for the heat equation on a convex set

DOI10.1090/mcom/3653zbMath1483.65128OpenAlexW3168891439MaRDI QIDQ4956924

Ryan I. Fernandes, Maksymilian Dryja, Bernard Bialecki

Publication date: 2 September 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3653

zbMATH Keywords

convergence analysisheat equationfinite differenceADI

Mathematics Subject Classification ID

Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Uses Software

• mctoolbox

Cites Work

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• A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
• The Peaceman-Rachford method for small mesh increments
• Convergence analysis of the finite difference ADI scheme for variable coefficient parabolic problems with nonzero Dirichlet boundary conditions
• Stability and Convergence of the Peaceman-Rachford ADI Method for Initial-Boundary Value Problems
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• A New Computational Procedure for A.D.I. Methods
• A Cartesian grid embedded boundary method for the heat equation on irregular domains

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