New explicit group iterative methods in the solution of three dimensional hyperbolic telegraph equations

In this paper, new group iterative numerical schemes based on the centred and rotated (skewed) seven-point finite difference discretisations are proposed for the solution of a three dimensional second order hyperbolic telegraph equation, subject to specific initial and Dirichlet boundary conditions....

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Bibliographic Details
Published inJournal of computational physics Vol. 294; pp. 382 - 404
Main Authors Kew, Lee Ming, Ali, Norhashidah Hj. Mohd
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2015
Subjects
Approximation
Complexity
Computation
Dirichlet problem
Explicit group methods
Finite difference
Iterative methods
Mathematical analysis
Mathematical models
Rotated grids
Three dimensional
Three dimensional telegraph equations
Unconditionally stable
Explicit group methods
Finite difference
Rotated grids
Three dimensional telegraph equations
Unconditionally stable
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Summary:In this paper, new group iterative numerical schemes based on the centred and rotated (skewed) seven-point finite difference discretisations are proposed for the solution of a three dimensional second order hyperbolic telegraph equation, subject to specific initial and Dirichlet boundary conditions. Both schemes are shown to be of second order accuracies and unconditionally stable. The scheme derived from the rotated grid stencil results in a reduced linear system with lower computational complexity compared to the scheme derived from the centred approximation formula. A comparative study with other common point iterative methods based on the seven-point centred difference approximation together with their computational complexity analyses is also presented.
Bibliography:ObjectType-Article-1
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content type line 23
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2015.03.052