The numerical treatment of nonlinear parabolic partial differential equations governing convection-diffusion processes

Abstract

An idea of Allen and Southwell [1] is adapted to the numerical solution of a nonlinear parabolic partial differential equation governing convection-diffusion pro­ cesses. This idea enables us to derive a spatial variable exponential fitting scheme. Using this scheme reduces the problem under consideration to a nonlinear system of ordinary differential equations. This system is solved by using three-level time schemes. The stability analysis for such schemes are carried out by the matrix method for initial boundary-value linear model. Sample of our numerical experiments are given and compared with other methods.

Keywords:

• Partial differential equations
• convection-diffusion
• exponential fit­ting
• time schemes
• stability

C.R. Categories:

• G1.8

^*At present: Department of Mathematics, The University, Doha, Qatar, P.O. Box 2713.

^*At present: Department of Mathematics, The University, Doha, Qatar, P.O. Box 2713.

Notes

^*At present: Department of Mathematics, The University, Doha, Qatar, P.O. Box 2713.