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Liouville-Green Transform Method for Linear Singular Perturbation Boundary Value Problems

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Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 131))

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Abstract

The numerical treatment of singular perturbation problems is currently a field in which active research is going on these days. Singular perturbation problems in which the term containing the highest order derivative is multiplied by a small parameter ε, occur in a number of areas of applied mathematics, science and engineering, among them fluid mechanics (boundary layer problems), elasticity (edge effect in shells) and quantum mechanics. In this paper, a linear singularly perturbed two-point boundary value problem with the boundary layer at left end point is solved. The given singularly perturbed two-point boundary value problem is replaced by Liouville-Green transform method. This transformed problem is solved. One linear numerical example has been solved to demonstrate the applicability of the method.

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Authors and Affiliations

  1. Department of Mathematics, Jaypee University of Engineering & Technology, Raghogarh, Guna, M.P, India, 473226

    Hradyesh Kumar Mishra

Authors
  1. Hradyesh Kumar Mishra
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Correspondence to Hradyesh Kumar Mishra .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, Roorkee, 247667, India

    Kusum Deep

  2. Department of Mathematics and, Computer Science, Liverpool Hope University, Hope Park, Liverpool, L16 9JD, United Kingdom

    Atulya Nagar

  3. , Department of Paper Technology, Indian Institute of Technology Roorkee, Uttarakhand, Roorkee, 247667, India

    Millie Pant

  4. Information Technology and Management, ABV-Indian Institute of, 109, E- Block, Gwalior, 474010, India

    Jagdish Chand Bansal

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Mishra, H.K. (2012). Liouville-Green Transform Method for Linear Singular Perturbation Boundary Value Problems. In: Deep, K., Nagar, A., Pant, M., Bansal, J. (eds) Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011. Advances in Intelligent and Soft Computing, vol 131. Springer, New Delhi. https://doi.org/10.1007/978-81-322-0491-6_94

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  • DOI: https://doi.org/10.1007/978-81-322-0491-6_94

  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-0490-9

  • Online ISBN: 978-81-322-0491-6

  • eBook Packages: EngineeringEngineering (R0)

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