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

We first describe a one-parameter family of unconditionally stable third-order time-integration schemes for the convection-diffusion equation: u t + cu x = vu xx , based on the extended trapezoidal formulas of Usmani and Agarwal [1]. Interestingly, there exists a method that is fourth order as well...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2000-02, Vol.39 (3), p.71-84
Main Authors: Chawla, M.M., Al-Zanaidi, M.A., Al-Aslab, M.G.
Format: Article
Language:English
Subjects:
Convection-diffusion equation
Crank-Nicolson method
Extended Simpson rules
Extended trapezoidal formulas
Finite-difference schemes
Unconditional stability
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Summary:We first describe a one-parameter family of unconditionally stable third-order time-integration schemes for the convection-diffusion equation: u t + cu x = vu xx , 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.
ISSN:0898-1221
1873-7668
DOI:10.1016/S0898-1221(99)00334-X