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A numerical application of the decomposition method for the combined KdV-MKdV equation. (English) Zbl 1080.65100

The authors consider solitary-wave solutions of the combined Korteweg-de Vries-modified Korteweg-de Vries (KdV-MKdV) equation. They prove the convergence of the Adomian decomposition method applied to the combined KdV-MKdV equation. Then they obtain the exact solitary-wave solutions and numerical solutions of the combined KdV-MKdV equations for the initial conditions. The numerical solutions are compared with the known analytical solutions.
This is a good adaptation of the Adomian method to a concrete partial differential equation. We suggest to the authors to solve partial differential equations with initial and boundary conditions.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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