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Zbl 1168.65376
Soliman, A.A.; Ali, A.H.A.; Raslan, K.R.
Numerical solution for the KdV equation based on similarity reductions. (English)
[J] Appl. Math. Modelling 33, No. 2, 1107-1115 (2009). ISSN 0307-904X

Summary: The present paper is devoted to the development of a new scheme to solve the KdV equation locally on sub-domains using similarity reductions for partial differential equations. Each sub-domain is divided into three-grid points. The ordinary differential equation deduced from the similarity reduction can be linearized, integrated analytically and then used to approximate the flux vector in the KdV equation. The arbitrary constants in the analytical solution of the similarity equation can be determined in terms of the dependent variables at the grid points in each sub-domain. This approach eliminates the difficulties associated with boundary conditions for the similarity reductions over the whole solution domain. Numerical results are obtained for two test problems to show the behavior of the solution of the problems. The computed results are compared with other numerical results.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35Q53 KdV-like equations

Keywords: KdV equation; finite difference methods; the similarity reductions

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