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Extended one-step time-integration schemes for convection-diffusion equations

✍ Scribed by M.M. Chawla; M.A. Al-Zanaidi; M.G. Al-Aslab

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
663 KB
Volume
39
Category
Article
ISSN
0898-1221

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✦ Synopsis

We first describe a one-parameter family of unconditionally stable third-order timeintegration schemes for the convection-diffusion equation: ut + cux = vuxx, based on the extended trapezoidal formulas of Usmani and Agarwal [1]. Interestingly, there exists a method that is .fourth order as well as unconditionally stable. We then describe a one-parameter family of unconditionally stable fourth-order time-integration schemes, based on the extended Simpson rules of Chawla et al. [2]. Again, there exists a method that is fifth order as well as unconditionally stable. The stability and accuracy of the obtained methods are tested, and compared with the widely used method of Crank-Nicolson, by considering three problems of practical interest. (~) 2000 Elsevier Science Ltd. All rights reserved.

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