Author(s)

W. K. Zahra^1,2, M. A. El-Beltagy³, A. M. El Mhlawy¹, R. R. Elkhadrawy¹

¹Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.
²Department of Mathematics, Basic and Applied Sciences Institute, Egypt-Japan University of Science and Technology, Alexandria, Egypt.
³Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, Egypt.

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.

Singular Perturbation Problem, Shishkin Mesh, Two Small Parameters, Exponential Spline, Interval Analysis, Sensitivity Analysis, Monte Carlo Simulations

Zahra, W. , El-Beltagy, M. , El Mhlawy, A. and Elkhadrawy, R. (2018) Exponential Spline Solution for Singularly Perturbed Boundary Value Problems with an Uncertain—But—Bounded Parameter. Journal of Applied Mathematics and Physics, 6, 854-863. doi: 10.4236/jamp.2018.64073.