Numerical approximation to the MEW equation for the single solitary wave and different types of interactions of the solitary waves

Abstract

The main motivation of the current study is to find out better approximate solutions of the modified equal width wave (MEW) equation. In order to achieve this aim, the power of two numerical methods are combined and an extended literature survey has been carried out. Quartic B-spline base functions have been utilized since the first-order and second-order weighting coefficients that are needed for space discretization are obtained directly. As test problems, twelve different applications of single solitary wave and four different applications of the interaction between the two solitary waves are solved successfully. All of the approximate solutions have been compared to nearly fifty various earlier applications existing in the literature. Also, the rate of the convergence is given with error norms. Comparisons show the fact that the current method obtains improved results than most of the common earlier methods.

Keywords:

• Finite difference method
• differential quadrature method
• solitary wave
• modified equal width equation
• convergence

AMS classifications:

• 65N06
• 65D32
• 65M12
• 74J35
• 65D07

Disclosure statement

No potential conflict of interest was reported by the author(s).