A new perspective for simulations of the equal-width wave equation

The fundamental aim of the present article is to numerically solve the non-linear Equal-Width Wave (EW) equation. For this purpose, the nonlinear term appearing in the equation is first linearized by a Rubin-Graves-type approach. After that, to reduce the equation into a solvable discretized linear algebraic equation system, which is the essential part of this study, the Crank-Nicolson-type approximation and cubic Hermite collocation method are respectively applied to obtain the integration in the temporal and spatial domain directions. To demonstrate how good the offered method is at generating approximate numerical results, six experimental problems exhibiting different wave profiles, known as the motion of a single, interacting two and three, the Maxwellian initial, undular bore, and colliding soliton waves given with different initial and boundary conditions of the EW equation, will be taken into consideration and solved. Since only the first model problem has an exact solution among these solitary waves, to measure error magnitudes, the widely used mean squared and maximum norms between analytical and approximate solutions are calculated and also compared with those from other existing works available in the literature. Furthermore, the three conservation constants known as mass, moment, and energy quantities are also computed and presented throughout the wave simulations with increasing time. In addition, a tabular comparison of the newly computed norms and conservation constants shows that the current scheme produces better and more compatible solutions than those of most of the previous works with the same parameters. Apart from that, the stability analysis for this present scheme has been illustrated using the von Neumann method.

کلیدواژه ها:

Equal-width wave equation ، cubic hermite collocation method ، solitary waves ، Stability analysis ، Crank-Nicolson type approximation ، Rubin-Graves type linearization