 Implicit locally one-dimensional methods for two-dimensional diffusion with a non-local boundary conditionMehdi Dehghan Mathematics and Computers in Simulation (MATCOM), 1999, vol. 49, issue 4, 331-349 Abstract: Two new second-order finite difference techniques based upon the classical 3-point backward time centered space (BTCS) method and the Crank–Nicolson scheme, and also a fourth-order finite difference scheme based on Crandall's method for one-dimensional diffusion, are used to solve the two-dimensional time dependent diffusion equation with non-local boundary conditions. In these cases locally one-dimensional (LOD) techniques are used to extend the one-dimensional techniques to solve the two-dimensional problem. The stability properties and truncation error of these methods are discussed and the results of a numerical experiment for these three methods are presented. Error estimates are also tabulated. The results of numerical testing shows that these schemes uses less central processor (CPU) time than the fully implicit schemes. Keywords: Finite differences schemes; Heat equation; LOD techniques; Non-local boundary value problems; Numerical integration techniques; Implicit methods; Partial differential equations; Stability CPU time (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:49:y:1999:i:4:p:331-349 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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