The solution of KdV and mKdV equations using Adomian Padé approximation. (English) Zbl 1401.65122

Abassy, Tamer A.; El-Tawil, Magdy A.; Saleh, Hassan K.

Int. J. Nonlinear Sci. Numer. Simul. 5, No. 4, 327-340 (2004).

Summary: Adomian Decomposition method (ADM) is an approximate method, which can be adapted to solve nonlinear partial differential equations. In this paper, we solve the KdV and modified KdV (mKdV) equations using ADM-Padé technique, which gives the approximate solution with fast convergence rate and high accuracy in the case of solitary wave solution and closed form solution in the case of rational polynomial solution.

MSC:

65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q53	KdV equations (Korteweg-de Vries equations)

Keywords:

KdV equation; mKdV equation; Adomian decomposition method (ADM); Padé approximants; ADM-Padé technique; solitary wave; Mathematica

Software:

Mathematica