Abstract
In this work we consider a system of singularly perturbed semilinear reaction-diffusion equations. To solve this problem numerically, we construct a finite difference scheme of Hermite type, and combine this with standard central difference scheme in a special way on a piecewise-uniform Shishkin mesh. We prove that the method is third order uniformly convergent. Numerical experiments are conducted to demonstrate the efficiency of the present method.
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Rao, S.C.S., Kumar, S. (2011). An Efficient Numerical Method for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_58
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DOI: https://doi.org/10.1007/978-3-642-18466-6_58
Publisher Name: Springer, Berlin, Heidelberg
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