Efficient numerical schemes for singularly perturbed parabolic initial-boundary-value problems |
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| Authors: | Srinivasan Natesan Rajdeep Deb |
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| Institution: | 1. Department of Mathematics, Indian Institute of Technology, Guwahati – 781 039, India;2. Department of Chemical Engineering, Indian Institute of Technology, Guwahati – 781 039, India |
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| Abstract: | In this article, we propose two efficient numerical schemes for singularly perturbed parabolic reaction-diffusion initialboundary-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. Numerical examples show ε -uniform convergence results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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