کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645780 | 1342063 | 2010 | 23 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Numerical solution of Boussinesq systems of the Bona–Smith family Numerical solution of Boussinesq systems of the Bona–Smith family](/preview/png/4645780.png)
In this paper we consider the one-parameter family of Bona–Smith systems, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a channel. We study numerically three initial-boundary-value problems for these systems, corresponding, respectively, to homogeneous Dirichlet, reflection, and periodic boundary conditions posed at the endpoints of a finite spatial interval. We approximate these problems using the standard Galerkin-finite element method for the spatial discretization and a fourth-order, explicit Runge–Kutta scheme for the time stepping, and analyze the convergence of the fully discrete schemes. We use these numerical methods as exploratory tools in a series of numerical experiments aimed at illuminating interactions of solitary-wave solutions of the Bona–Smith systems, such as head-on and overtaking collisions, and interactions of solitary waves with the boundaries.
Journal: Applied Numerical Mathematics - Volume 60, Issue 4, April 2010, Pages 314-336