Premium
The general analytical and numerical solution for the modified KdV equation with convergence analysis
Author(s) -
Rostamy D.,
Zabihi F.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2647
Subject(s) - mathematics , korteweg–de vries equation , hypercomplex number , homotopy analysis method , numerical analysis , mathematical analysis , runge–kutta methods , convergence (economics) , homotopy , pure mathematics , nonlinear system , geometry , physics , quantum mechanics , economics , quaternion , economic growth
We investigate the analytical and numerical solutions of the modified Kortweg de Vries equation by applying the idea of commutative hypercomplex mathematics, He's homotopy perturbation method as a simple particular procedure, and the Runge–Kutta discontinuous Galerkin methods. Moreover, we discuss at great length the convergence conditions for this equation by using the Banach fixed point theory, which could provide a good iteration algorithm. Finally, we compare the homotopy perturbation method with some standard ideas same as the Runge–Kutta discontinuous Galerkin method by some numerical illustrations. Copyright © 2012 John Wiley & Sons, Ltd.