A new method for a generalized Hirota–Satsuma coupled KdV equation

In this paper, differential transform method (DTM), which is one of the approximate methods is implemented for solving the nonlinear Hirota–Satsuma coupled KdV partial differential equation. A variety of initial value system is considered, and the convergence of the method as applied to the Hirota–S...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-05, Vol.217 (17), p.7117-7125
Main Authors: Xie, Manlin, Ding, Xuanhao
Format: Article
Language:English
Subjects:
Absolute error
Algorithms
Approximation
Convergence
Differential equations
Differential transform method
Exact sciences and technology
Generalized Hirota–Satsuma coupled KdV equation
Mathematical analysis
Mathematical models
Mathematics
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Solitary wave solution
Transforms
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Summary:In this paper, differential transform method (DTM), which is one of the approximate methods is implemented for solving the nonlinear Hirota–Satsuma coupled KdV partial differential equation. A variety of initial value system is considered, and the convergence of the method as applied to the Hirota–Satsuma coupled KdV equation is illustrated numerically. The obtained results are presented and only few terms of the expansion are required to obtain the approximate solution which is found to be accurate and efficient. Numerical examples are illustrated the pertinent features of the proposed algorithm.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.01.048