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Numerical treatment of singularly perturbed two point boundary value problems using initial-value method

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Abstract

In this paper, we describe an initial-value method for linear and nonlinear singularly perturbed boundary value problems in the interval [p,q]. For linear problems, the required approximate solution is obtained by solving the reduced problem and one initial-value problems directly deduced from the given problem. For nonlinear problems the original second-order nonlinear problem is linearized by using quasilinearization method. Then this linear problem is solved as previous method. The present method has been implemented on several linear and non-linear examples which approximate the exact solution. We also present the approximate and exact solutions graphically.

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, 211004, UP, India

    Manoj Kumar, Hradyesh Kumar Mishra & P. Singh

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  1. Manoj Kumar
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  2. Hradyesh Kumar Mishra
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  3. P. Singh
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Correspondence to Hradyesh Kumar Mishra.

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Kumar, M., Mishra, H.K. & Singh, P. Numerical treatment of singularly perturbed two point boundary value problems using initial-value method. J. Appl. Math. Comput. 29, 229–246 (2009). https://doi.org/10.1007/s12190-008-0127-3

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  • DOI: https://doi.org/10.1007/s12190-008-0127-3

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