Non-Oscillatory Solution of a Singularly Perturbed Problem on Hybrid Shishkin-Exponential Expanding Mesh

Authors

  • Aslam Abdullah , Mohd Azahari Razali

Abstract

Mesh structure is one of important criteria that needs to be taken into consideration in
engineering numerical computation, particularly in the computation of fluid flows involving the discretized
governing equations. No single numerical scheme used to solve the algebraic forms of partial differential
equations which can stand alone without the mesh on which the solutions are calculated. An appropriate
mesh ensures a numerical scheme to work effectively. Thus wide range of meshes proposed by researchers,
if not carefully applied, might lead to problems of accuracy, computation time, or even non-physical
solutions. We investigate in this research the practicality of a proposed hybrid Shishkin-exponential
expanding mesh and compare the results against the solutions on Shishkin mesh in highlighting the
significance of the mesh structure in numerical solution of a singularly perturbed problem. In particular, we
apply a systematic technique in setting both the singular perturbation parameter and mesh number. We
present the condition to avoid spurious oscillatory solutions on Shishkin mesh which depends on the
parameters of interest. This is done by adopting reasonable mesh interval sizes. The results of test cases
affirm that whenever the Shishkin mesh fails to support the non-oscillatory solutions, the Shishkinexponential expanding mesh might not.

Published

2020-04-30

Issue

Section

Articles