A Computational Method For Solving Singularly Perturbed Initial Value Problems
Department of Mathematics, Anna University of Technology, Tirunelveli - 627007, Tamil Nadu, India. E-mail: firstname.lastname@example.org
A computational method is presented for solving singularly perturbed initial value problems with an initial layer on the left end point of the interval. It is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems easy to use, modest problem preparation and ready computer implementation. The zeroth order asymptotic expansion is used to obtain the terminal boundary condition. Then, a initial layer region and a non-initial layer region are created. And so, the given problem is split into two initial value problems. All these problems are efficiently solved by an uniform and optimal exponentially fitted finite difference scheme. Error estimates for the computational method is derived using maximum principle,. Numerical results are given in this paper to demonstrate the applicability of the computational method.
Keywords: singular perturbation problems, exponentially fitted, uniformly convergent, asymptotic expansion, finite difference schemes.
AMS (MOS) subject classification: 65F05, 65N30, 65N35, 650Y05.
International eJournal of Mathematics and Engineering
Volume 3, Issue 2, Pages: 1487 - 1501