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Fourth-, Fifth-, Sixth-Order Linear Differential Equations (LDEs) via Homotopy Perturbation Method Using Laplace Transform

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Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 817))

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Abstract

In this article, we construct the solution of fourth-, fifth-, and sixth-order boundary value problems. To solve these boundary value problems, we apply the homotopy perturbation method (HPM) using Laplace transform (LT). The proposed method is easy, effective, and the accuracy of this method has been proved by comparing the results with homotopy perturbation method (HPM), variational iterative method (VIM), Adomian decomposition method (ADM), and exact solutions by using Mathematica package. The results obtained by this LT-HPM have been shown in tables and graphs.

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Acknowledgements

The second author is very much thankful for grant no. 1013/CST/R&D/Phy&EnggSc/2015 given by Madhya Pradesh Council of Science and Technology (MPCST), Bhopal, India.

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Authors and Affiliations

  1. Department of Mathematics, Jaypee University of Engineering and Technology, Guna, 473226, Madhya Pradesh, India

    Rajnee Tripathi & Hradyesh Kumar Mishra

Authors
  1. Rajnee Tripathi
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  2. Hradyesh Kumar Mishra
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Corresponding author

Correspondence to Hradyesh Kumar Mishra .

Editor information

Editors and Affiliations

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

    Jagdish Chand Bansal

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

    Kedar Nath Das

  3. Department of Mathematics and Computer Science, Faculty of Science, Liverpool Hope University, Liverpool, UK

    Atulya Nagar

  4. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  5. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, Odisha, India

    Akshay Kumar Ojha

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Tripathi, R., Mishra, H.K. (2019). Fourth-, Fifth-, Sixth-Order Linear Differential Equations (LDEs) via Homotopy Perturbation Method Using Laplace Transform. In: Bansal, J., Das, K., Nagar, A., Deep, K., Ojha, A. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 817. Springer, Singapore. https://doi.org/10.1007/978-981-13-1595-4_54

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