Improvement on stability and convergence of ADI schemes

DOI10.1007/BF02459276zbMath0931.65095OpenAlexW2076688751MaRDI QIDQ1305392

Aijie Cheng

Publication date: 15 February 2000

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02459276

zbMATH Keywords

stabilityconvergencealternating direction implicit schemesvariable coefficientquasilinear parabolic problemPeaceman-Rachford scheme\(H^{1} \) energy estimating methodDouglas scheme

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear parabolic equations (35K55) 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)

Cites Work

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• A priori estimates for the solutions of difference approximations to parabolic partial differential equations
• Alternating direction and semi-explicit difference methods for parabolic partial differential equations
• Alternating direction methods for three space variables
• A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
• The Numerical Solution of Parabolic and Elliptic Differential Equations

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