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A robust computational technique for a system of singularly perturbed reaction–diffusion equations

Kumar V., Bawa R. K., Lal A. K.

International Journal of Applied Mathematics and Computer Science

2014

Vol. 24, no. 2

387--395

In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the theoretical results.

Singularly perturbed systems of Volterra equations

Bijura A. M.

Journal of Applied Analysis

2002

Vol. 8, nr 2

221-244

Singularly perturbed linear Volterra integral equations are solved in this paper. To improve the results which has been published earlier, formal solutions of systems of equations are determined and rigorously proved to be asymptotic to the exact solutions.

Weierstrass theorems in strong asymptotic analysis

Mozo-Fernandez J.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 3

255-268

Some properties of the holomorphic functions defined in polysectors in [C^n] having an asymptotic development at the origin, in Mlajima's sense, are studied. We extend the Weierstrass preparation and division theorems to this context, in full generality, supposing that the domain of the "division variable" is a disc. We remove this condition if n = 2, but we need additional hypothesis. The Gevrey case is also studied.