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

Authors:
Samir Karaa;Mohamed Othman
Affiliations:
Department of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, Al-Khod 123, Muscat, Oman;Department of Communication Tech. and Networks, University Putra Malaysia, 43400 UPM Serdang, Selangor D.E., Malaysia
Venue:
Computers & Mathematics with Applications
Year:
2009

Citing 5
Cited 1

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
High order difference schemes for unsteady one-dimensional diffusion-convection problems

Journal of Computational Physics
Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients

Journal of Computational and Applied Mathematics
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
High order ADI method for solving unsteady convection-diffusion problems

Journal of Computational Physics

Combined compact difference scheme for linear second-order partial differential equations with mixed derivative

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.09

Visualization

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 @m. Numerical results with @m=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.