The Galerkin method for the KdV equation using a new basis of smooth piecewise cubic polynomials

The Galerkin method for the KdV equation using a new basis of smooth piecewise cubic polynomials

In this paper, we introduce the Galerkin method using a new basis of smooth piecewise cubic polynomials for the one-dimensional nonlinear KdV equation. The stability analysis shows that the present method is unconditionally stable in L2-norm. Numerical experiments show that the proposed method prese...

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Veröffentlicht in:Applied mathematics and computation 2012-05, Vol.218 (17), p.8659-8671
Hauptverfasser: Hao, Shu-Yan, Xie, Shu-Sen, Yi, Su-Cheol
Format: Artikel
Sprache:eng
Schlagworte:
Computer simulation
Conservation law
Conservation laws
Galerkin methods
Mathematical analysis
Mathematical models
Nonlinearity
Preserves
Smooth piecewise cubic polynomial
Solitary waves
Stability
The Galerkin method
The KdV equation
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Beschreibung
Zusammenfassung:In this paper, we introduce the Galerkin method using a new basis of smooth piecewise cubic polynomials for the one-dimensional nonlinear KdV equation. The stability analysis shows that the present method is unconditionally stable in L2-norm. Numerical experiments show that the proposed method preserves the conservation laws and is effective for simulating the motions and the interactions of solitary waves.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2012.02.027