Abstract
Our main purpose in this work is to investigate a new solution that represents a numerical behavior for one well-known nonlinear wave equation, which describes the Bona–Smith family of Boussinesq type. A numerical solution has been obtained according to the quintic B-spline collocation method. The method is based on the Crank–Nicolson formulation for time integration and quintic B-spline functions for space integration. The stability of the proposed method has been discussed and presented to be unconditionally stable. The efficiency of the proposed method has been demonstrated by studying a solitary wave motion and interaction of two and three solitary waves. The results are found to be in good agreement with the analytic solution of the system. We demonstrated the physical interpretation of some obtained results graphically with symbolic computation.
The exponential cubic B-spline collocation method for the Kuramoto-Sivashinsky equation