Numerical treatment of fourth order singularly perturbed boundary value problems

Authors:
Basem S. Attili
Affiliations:
Department of Mathematics and Computer Science, U. A. E. U. – College of Science, Al-Ain, United Arab Emirates
Venue:
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Year:
2004

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Abstract

A numerical algorithm is proposed to solve a class of fourth order singularly perturbed two point boundary value problems (BVP). The method starts by transforming the BVP into a system of two second order ordinary differential equations with appropriate boundary conditions. The interval over which the BVP is defined will be subdivided into three disjoint regions. The system will then be solved separately on each subinterval. We combine the obtained solutions to get the solution of the BVP over the entire interval. For the inner regions, the boundary conditions at the end points are obtained through the zero order asymptotic expansion of the solution of the BVP. Examples will be solved to demonstrate the method and its efficiency.