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Zbl 1068.65119
Kaya, Doǧan; Inan, Ibrahim E.
A convergence analysis of the ADM and an application. (English)
[J] Appl. Math. Comput. 161, No. 3, 1015-1025 (2005). ISSN 0096-3003

The Adomian decomposition method (ADM) is applied to the modified Korteweg-de Vries equation. This method yields exact and approximate solutions of nonlinear problems without transforming the equation. The solution is expressed in a series and the basis functions are obtained via recursions. Several analytical solutions for the modified Korteweg-de Vries homogeneous and inhomogeneous equation are given. The numerical convergence of the method is illustrated by an example and sufficient conditions of convergence are proven.
[Kai Schneider (Marseille)]

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35Q53 KdV-like equations
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: modified Korteweg-de Vries equation; exact solutions; convergence; Adomian decomposition method; numerical example

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