Abstract
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.
Highlights
In recent years, remarkable developments have taken place in the study of nonlinear evolutionary partial differential equations
We study the accuracy of the proposed method by calculating the infinity error norm
All numerical results are obtained from the solution of the nonlinear schemes (19) and (20) using Newton’s method
Summary
Remarkable developments have taken place in the study of nonlinear evolutionary partial differential equations. It is realized that many such equations possess special solutions in the form of pulses which retain their shapes and velocities after interacting with each other. Most of the current research is directed to solve coupled nonlinear systems analytically and numerically [9,10,11,12,13,14,15,16,17,18,19,20,21]. Solitons are of great interest in many physical areas, as, for example, in dislocation theory of crystals, plasma and fluid dynamics, magnetohydrodynamics, laser and fiber optics, and the study of the water waves
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