A Novel Approach for Simulations of EW Equation by Trigonometric Collocation Method

Year 2026, Volume: 7 Issue: 1, 70 - 90, 31.01.2026

Ali Sercan Karakaş , Murat Yağmurlu

Abstract

The current manuscript primarily aims to derive a novel scheme of the Equal Width (EW) wave equation by applying the finite element method, one of the approximation methods, to obtain its algorithm and write its code with the help of an appropriate symbolic programming language, and then to compare the results obtained from the simulation with the results that have been obtained in the past and brought to the literature in the light of the data obtained from their simulations. In order to test the program code that is obtained by schematizing the equation, 5 test problems are going to be simulated. These are single-wave, two-wave, three-wave interference, Maxwellian and undular bore. Of these, only the single-wave interference has got the exact solution, so the widely used error norms L₂ and L_{∞} are computed in the results for this single-wave interference. Since the analytical solution of the other problems is not available, the conservation constants are computed to compare the simulation data. In order to enable other scientists to analyze the simulation data appropriately, the tables and graphs based on the simulation data are presented. From these comparisons, it could be easily seen that the present scheme may be implemented for other linear or nonlinear equations encountered in nature.The computed results verify that the suggested algorithm has the advantage of obtaining a highly accurate approximate solution of the EW equation as compared to the existing methods. The main purpose of using this method here is to try to achieve better results with a highyield low-cost approach method by getting rid of the high speed and storage cost requirements caused by traditional usages

Keywords

Collocation Finite Element method , solitary waves , quintic trigonometric B-splines , wave simulations , Linearization

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