Multilevel difference schemes for the heat conduction equation and its application to the Dirichlet problem in two and three dimensions

DOI10.1007/BF02575924zbMath0433.65051OpenAlexW2025247555MaRDI QIDQ1139361

S. H. Smith

Publication date: 1979

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02575924

zbMATH Keywords

stabilitynumerical exampleDirichlet problemerror boundscharacteristic equationADI methodsheat conduction equationmultilevel schemesiteration parametersiteration cycles

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

Cites Work

• A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
• On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
• A Survey of Numerical Methods for Parabolic Differential Equations
• On the Structure of Alternating Direction Implicit (A.D.I.) and Locally One Dimensional (L.O.D.) Difference Methods
• Two High-Order Correct Difference Analogues for the Equation of Multidimensional Heat Flow
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