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Differential Quadrature Method for Solving Fifth-Order KdV Equations

  • P. KarunakarEmail author
  • S. Chakraverty
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (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.

Keywords

Differential Quadrature Method Korteweg–de-Vries equations Shallow Water Waves Shifted Legendre polynomials 

Notes

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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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of Technology RourkelaRourkelaIndia

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