Parameter uniform numerical method for fourth order singularly perturbed turning point problems exhibiting boundary layers

N. Geetha, A. Tamilselvan
2016 Ain Shams Engineering Journal  
In this paper, a numerical method based on Shishkin mesh for a singularly perturbed fourth order differential equation with a turning point exhibiting boundary layers is presented. In this method the problem is transformed into a weakly coupled system of two second order equations, one without the parameter e and the other with the parameter e multiplying the highest derivative with suitable boundary conditions. We apply classical finite difference scheme on an appropriate piecewise uniform
more » ... ecewise uniform (Shishkin) mesh. Parameter uniform error bounds for the numerical solution are established. Numerical results are provided to illustrate the theoretical results. Ó 2016 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
doi:10.1016/j.asej.2016.04.018 fatcat:nnwbtnmcyfabbcvtdnmdy2ycqq