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Kaya, Doǧan

An explicit and numerical solutions of some fifth-order KdV equation by decomposition method. (English) Zbl 1024.65096

Appl. Math. Comput. 144, No. 2-3, 353-363 (2003).
Summary: By considering the Adomian decomposition method, explicit and numerical solutions are calculated for a various fifth-order Korteweg-de Vries (KdV) equations with initial condition. The method does not need linearization or weak nonlinearity assumptions, perturbation theory. The decomposition series explicit solution of the equation is quickly obtained by observing the existence of the self-canceling “noise” terms where sum of components vanishes in the limit.

Cited in 49 Documents

MSC:

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

Keywords:

Adomian decomposition method; fifth-order KdV equation; Kawahara equation; self-canceling noise terms; numerical examples; Korteweg-de Vries equations

Software:

ATFM
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\textit{D. Kaya}, Appl. Math. Comput. 144, No. 2--3, 353--363 (2003; Zbl 1024.65096)
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References:

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