Department of Mathematics, Faculty of Arts and Sciences, Inonu University, Malatya, Turkey.
10.22034/cmde.2025.62400.2747
Abstract
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 firstly linearized by 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 generates approximate numerical results, six experimental problems exhibiting different wave profiles known as the motion of 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 used widely 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 show that the current scheme produces better and compatible solutions than those of the most of the previous works with the same parameters. Apart from those, the stability analysis for this present scheme has been illustrated using the von Neumann method.
Kutluay, S. , Yağmurlu, N. Murat and Karakaş, A. Sercan (2025). A New Perspective for Simulations of Equal-Width Wave Equation. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.62400.2747
MLA
Kutluay, S. , , Yağmurlu, N. Murat, and Karakaş, A. Sercan. "A New Perspective for Simulations of Equal-Width Wave Equation", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.62400.2747
HARVARD
Kutluay, S., Yağmurlu, N. Murat, Karakaş, A. Sercan (2025). 'A New Perspective for Simulations of Equal-Width Wave Equation', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.62400.2747
CHICAGO
S. Kutluay , N. Murat Yağmurlu and A. Sercan Karakaş, "A New Perspective for Simulations of Equal-Width Wave Equation," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.62400.2747
VANCOUVER
Kutluay, S., Yağmurlu, N. Murat, Karakaş, A. Sercan A New Perspective for Simulations of Equal-Width Wave Equation. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.62400.2747
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