Assist. Prof. Dr. waheed zahra

University: Tanta University
Department: Department of Physics and Engineering Mathematics
Research Fields: •Numerical methods, analysis and computation •Numerical solution of Differential Equations (Ordinary - Fractional) •Numerical solution of Partial Differential Equations •Applications of numerical methods to science and engineering

Abstracts

1 Exponential Spline Solution for Singularly Perturbed Boundary Value Problems with an Uncertain-But-Bounded Parameter

Authors: waheed zahra, Mohamed El-Beltagy, Ashraf El Mhlawy, Reda Elkhadrawy

Abstract:

In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order.

Keywords: Sensitivity Analysis, interval analysis, singular perturbation problem, shishkin mesh, two small parameters, exponential spline

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