TITLE:
Exponential Spline Solution for Singularly Perturbed Boundary Value Problems with an Uncertain—But—Bounded Parameter
AUTHORS:
W. K. Zahra, M. A. El-Beltagy, A. M. El Mhlawy, R. R. Elkhadrawy
KEYWORDS:
Singular Perturbation Problem, Shishkin Mesh, Two Small Parameters, Exponential Spline, Interval Analysis, Sensitivity Analysis, Monte Carlo Simulations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.4,
April
25,
2018
ABSTRACT: In this paper, we develop a new numerical method
which is based on an exponential spline and Shishkin mesh discretization to
solve singularly perturbed boundary value problems, which contain a small
uncertain perturbation parameter. The proposed method uses interval analysis
principle to deal with the uncertain parameter and the Monte Carlo Simulations
(MCS) are used to validate the solution and the accuracy of the proposed
method. Furthermore, sensitivity analysis has been conducted using different
methods to assess how much the solution is sensitive to the changes of the
perturbation parameter. Numerical results are provided to show the applicability
and efficiency of the proposed method, which is ε-uniform convergence of almost second order.