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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.

An application of the Choquet theorem to the study of randomly-superinvariant measures

Rajba T.

Opuscula Mathematica

2012

Vol. 32, no. 2

317-326

Given a real valued random variable Θ we consider Borel measures μ on Β (R), which satisfy the inequality μ(B) ≥ Eμ (B-Θ) (B ∈ Β (R)) or the integral inequality [formula].We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable Θ.