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Differential Quadrature Method for Solving Fifth-Order KdV Equations

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Recent Trends in Wave Mechanics and Vibrations

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

The third- and fifth-order Korteweg–de-Vries (KdV) equations are the commonly used models for the study of various fields of science and engineering, viz., Shallow Water Waves (SWW) with surface tension and magnetoacoustic waves, etc. It is not easy to find the analytical solutions of physical models when they are highly nonlinear. As such, this article aims to find the numerical solutions of fifth-order KdV equations using Differential Quadrature Method (DQM). In DQM, shifted Legendre polynomials-based grid points have been used in finding the solution of two types of fifth-order KdV equations. The present results by DQM are compared with results obtained by other methods. Finally, error plot has also been incorporated and carried out to see the effect of number of grid points on the solution of fifth-order KdV equations.

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Acknowledgements

The authors are thankful to the Board of Research in Nuclear Sciences (BRNS), Mumbai, India for the support to carry out the present research work.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769 008, Odisha, India

    P. Karunakar & S. Chakraverty

Authors
  1. P. Karunakar
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  2. S. Chakraverty
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Correspondence to P. Karunakar .

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Editors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India

    S. Chakraverty

  2. Vibration Research Group, Von karman society, Jalpaiguri, India

    Paritosh Biswas

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Karunakar, P., Chakraverty, S. (2020). Differential Quadrature Method for Solving Fifth-Order KdV Equations. In: Chakraverty, S., Biswas, P. (eds) Recent Trends in Wave Mechanics and Vibrations. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-0287-3_26

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  • DOI: https://doi.org/10.1007/978-981-15-0287-3_26

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-0286-6

  • Online ISBN: 978-981-15-0287-3

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