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

Samir Karaa*, Mohamed Othman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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
Issue number2
Publication statusPublished - Jul 2009


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

ASJC Scopus subject areas

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


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