Differential Quadrature Method for Solving Fifth-Order KdV Equations
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.
KeywordsDifferential Quadrature Method Korteweg–de-Vries equations Shallow Water Waves Shifted Legendre polynomials
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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