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A comparison between two different methods for solving KdV-Burgers equation. (English) Zbl 1084.65079
Summary: This paper presents two methods for finding the soliton solutions to the nonlinear dispersive and dissipative KdV-Burgers equation. The first method is a numerical one, namely the finite differences with variable mesh. The stability of the numerical scheme is discussed. The second method is the semi-analytic Adomian decomposition method. Test example is given. A comparison between the two methods is carried out to illustrate the pertinent feature of the proposed algorithm.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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