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Ismail, M. S.; Mosally, Farida

A fourth order finite difference method for the good Boussinesq equation. (English) Zbl 1470.65151

Abstr. Appl. Anal. 2014, Article ID 323260, 10 p. (2014).
Summary: The “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. Head-on and overtaking interactions of two solitons are also considered. The numerical results reveal the good performance of the derived method.

Cited in 11 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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