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ORIGINAL PAPER
An Intial-Value Technique for Self-Adjoint Singularly Perturbed Two-Point Boundary Value Problems
1
Department of Mathematics, Prasad V Potluri Siddhartha Institute of Technology, Vijayawada-, 520007, Andhra Pradesh, India
2
Department of Mathematics, VNR VignanaJyothi Institute of Engineering and Technology, Kukatpally, Hyderabad – , 500090, India
3
Department of Mechanical Engineering, Cleveland State University, Cleveland, USA
Online publication date: 2020-03-12
Publication date: 2020-03-01
International Journal of Applied Mechanics and Engineering 2020;25(1):106-126
KEYWORDS
ABSTRACT
In this paper, we present an initial value technique for solving self-adjoint singularly perturbed linear boundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value problems. This replacement is significant from the computational point of view. The classical fourth order Runge-Kutta method is used to solve these initial value problems. This approach to solve singularly perturbed boundary-value problems is numerically very appealing. To demonstrate the applicability of this method, we have applied it on several linear examples with left-end boundary layer and right-end layer. From the numerical results, the method seems accurate and solutions to problems with extremely thin boundary layers are obtained.
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