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 |
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| container_title | Applied mathematics and computation |
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| creator | Hao, Shu-Yan Xie, Shu-Sen Yi, Su-Cheol |
| description | 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. |
| doi_str_mv | 10.1016/j.amc.2012.02.027 |
| format | Article |
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| ispartof | Applied mathematics and computation, 2012-05, Vol.218 (17), p.8659-8671 |
| issn | 0096-3003 1873-5649 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | 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 |
| title | The Galerkin method for the KdV equation using a new basis of smooth piecewise cubic polynomials |
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