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

• Published in: Applied mathematics and computation Vol. 217; no. 17; pp. 7117 - 7125
• Main Authors: Xie, Manlin, Ding, Xuanhao
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.05.2011; Elsevier
• 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; Absolute error; Generalized Hirota–Satsuma coupled KdV equation; Solitary wave solution; Differential transform method; Convergence; Approximate method; Error estimation; Generalized Hirota-Satsuma coupled KdV equation; Initial value problem; Algorithm; Partial differential equation; Implementation; Korteweg de Vries equation; Numerical analysis; Boundary value problem; Applied mathematics
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2011.01.048

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.