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Fourth‐order exponential finite difference methods for boundary value problems of convective diffusion type
Author(s) -
Radhakrishna Pillai A. C.
Publication year - 2001
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.167
Subject(s) - mathematics , exponential function , diagonal , finite difference , finite difference method , boundary value problem , mathematical analysis , constant (computer programming) , boundary (topology) , geometry , computer science , programming language
Methods based on exponential finite difference approximations of h 4 accuracy are developed to solve one and two‐dimensional convection–diffusion type differential equations with constant and variable convection coefficients. In the one‐dimensional case, the numerical scheme developed uses three points. For the two‐dimensional case, even though nine points are used, the successive line overrelaxation approach with alternating direction implicit procedure enables us to deal with tri‐diagonal systems. The methods are applied on a number of linear and non‐linear problems, mostly with large first derivative terms, in particular, fluid flow problems with boundary layers. Better accuracy is obtained in all the problems, compared with the available results in the literature. Application of an exponential scheme with a non‐uniform mesh is also illustrated. The h 4 accuracy of the schemes is also computationally demonstrated. Copyright © 2001 John Wiley & Sons, Ltd.