Application of HAM to seventh order KdV equations

Rajan Arora () and Hariom Sharma ()
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Rajan Arora: IIT Roorkee
Hariom Sharma: IIT Roorkee

International Journal of System Assurance Engineering and Management, 2018, vol. 9, issue 1, No 15, 138 pages

Abstract: Abstract In this paper, the homotopy analysis method (HAM) is applied to obtain the approximate solutions of KdV equations of seventh order, which are Sawada Kotera Ito equation, Lax equation, and Kaup–Kuperschmidt equation, respectively. The convergence of the homotopy analysis method is discussed with the help of auxiliary parameter h, which controls the convergence of the method and also called as the convergence control parameter. The results obtained by the HAM are compared with the exact solutions, by fixing the value of arbitrary constant. It is found that HAM is very robust and elegant method, and by choosing a suitable value of h we can get the approximate solution in very few iteration. Computations are performed with the help of symbolic computation package MATHEMATICA.

Keywords: The Sawada–Kotera–Ito equation; Lax equation; Kaup–Kuperschmidt equation; Homotopy analysis method; Approximate numerical solutions; Symbolic computation (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13198-016-0490-7

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