On the accuracy of a finite-difference method for parabolic partial differential equations with discontinuous boundary conditions

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Abstract

Although the numerical solution of parabolic partial differential equations (PDEs) is widely documented, the effect of discontinuous boundary conditions on numerical accuracy is not. This article employs the Keller box finite-difference method to study the effect of such discontinuities when solving the linear one-demensional transient heat equation. We demonstrate that this formally second-order-accurate scheme can lose accuracy, but that an analytical understanding of the behavior of the solution helps in providing an accuracy-restoring formulation. Benchmark computations are presented that will provide guidance in the numerical solution of nonlinear parabolic PDEs for which there are no closed-form analytical solutions.

Original languageEnglish
Pages (from-to)275-292
Number of pages18
JournalNumerical Heat Transfer, Part B: Fundamentals
Volume64
Issue number4
DOIs
Publication statusPublished - 1 Oct 2013

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