Two-level compact implicit schemes for three-dimensional parabolic problems

Samir Karaa, Mohamed Othman

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We derive a class of two-level high-order implicit finite difference schemes for solving three-dimensional parabolic problems with mixed derivatives. The schemes are fourth-order accurate in space and second- or lower-order accurate in time depending on the choice of a weighted average parameter μ. Numerical results with μ = 0.5 are presented to confirm the high accuracy of the derived scheme and to compare it with the standard second-order central difference scheme. It is shown that the improvement in accuracy does not come at a higher cost of computation and storage since it is possible to choose the grid parameters so that the present scheme requires less work and memory and gives more accuracy than the standard central difference scheme.

Original languageEnglish
Pages (from-to)257-263
Number of pages7
JournalComputers and Mathematics with Applications
Volume58
Issue number2
DOIs
Publication statusPublished - Jul 2009

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Compact Scheme
Implicit Scheme
Parabolic Problems
Central Difference Schemes
Three-dimensional
Weighted Average
Derivatives
Data storage equipment
Finite Difference Scheme
Fourth Order
High Accuracy
Choose
Higher Order
Grid
Costs
Derivative
Numerical Results
Standards

Keywords

  • Crank-Nicolson integrator
  • High-order compact scheme
  • Mixed derivative
  • Parabolic partial differential equation
  • Stability

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Modelling and Simulation
  • Computational Mathematics

Cite this

Two-level compact implicit schemes for three-dimensional parabolic problems. / Karaa, Samir; Othman, Mohamed.

In: Computers and Mathematics with Applications, Vol. 58, No. 2, 07.2009, p. 257-263.

Research output: Contribution to journalArticle

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