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Section B

Higher-order time accurate numerical methods for singularly perturbed parabolic partial differential equations

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Pages 1204-1214 | Received 26 Feb 2007, Accepted 01 Nov 2007, Published online: 17 Jun 2009
 

Abstract

This article presents two numerical methods for singularly perturbed time-dependent reaction-diffusion initial–boundary-value problems. The spatial derivative is replaced by a hybrid scheme, which is a combination of the cubic spline and the classical central difference scheme in both the methods. In the first method, the time derivative is replaced by the Crank–Nicolson scheme, whereas in the second method the time derivative is replaced by the extended-trapezoidal scheme. These schemes are applied on the layer resolving piecewise-uniform Shishkin mesh. Some numerical examples are carried out to show the accuracy and efficiency of these methods.

2000 AMS Subject Classification :

CCS Category :

Acknowledgements

This work is supported by the Department of Science and Technology, Government of India under research grant SR/S4/MS:318/06.

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