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A convergence analysis of the ADM and an application. (English) Zbl 1068.65119
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.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
65M12Stability and convergence of numerical methods (IVP of PDE)