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A Second Order Non-uniform Mesh Discretization for the Numerical Treatment of Singular Two-Point Boundary Value Problems with Integral Forcing Function

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Proceedings of Sixth International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 547))

Abstract

In the present work, we examine the three-point numerical scheme for the non-linear second order ordinary differential equations having integral form of forcing function. The approximations of solution values are obtained by means of finite difference scheme based on a special type of non-uniform meshes. The derivatives as well as integrals are approximated with simple second order accuracy both on uniform meshes and non-uniform meshes. A brief convergence analysis based on irreducible and monotone behaviour of Jacobian matrix to the numerical scheme is provided. The scheme is then tested on linear and non-linear examples that justify the order and accuracy of the new method.

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Acknowledgments

Science and Engineering Research Board, Department of Science and Technology, Government of India (No. SR/FTP/MS-020/2011) has supported the present research work.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, South Asian University, Chanakyapuri, 110 021, New Delhi, India

    Navnit Jha

Authors
  1. Navnit Jha
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Correspondence to Navnit Jha .

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Editors and Affiliations

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

    Kusum Deep

  2. Department of Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

  3. Department of Mathematics, National Institute of Technology, Silchar, Silchar, Assam, India

    Kedar Nath Das

  4. School of Mathematics, Thapar Institute of Engineering and Technology University, Patiala, Punjab, India

    Arvind Kumar Lal

  5. School of Mathematics, Thapar Institute of Engineering and Technology University, Patiala, Punjab, India

    Harish Garg

  6. Department of Mathematics and Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya K. Nagar

  7. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, India

    Millie Pant

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Jha, N. (2017). A Second Order Non-uniform Mesh Discretization for the Numerical Treatment of Singular Two-Point Boundary Value Problems with Integral Forcing Function. In: Deep, K., et al. Proceedings of Sixth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 547. Springer, Singapore. https://doi.org/10.1007/978-981-10-3325-4_39

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  • DOI: https://doi.org/10.1007/978-981-10-3325-4_39

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3324-7

  • Online ISBN: 978-981-10-3325-4

  • eBook Packages: EngineeringEngineering (R0)

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