A Petrov-Galerkin approach for the numerical analysis of soliton and multi-soliton solutions of the Kudryashov-Sinelshchikov equation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 مرداد 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.87548.1422

نویسندگان

hayat samy¹؛ waleed adel^{* 2، 3}؛ Ibrahim hanafy¹؛ Moataz Ramadan¹

¹Department of Mathematics and Computer Sciences, Faculty of Science, Port-Said University, Egypt.

²Laboratoire Interdisciplinaire de l’Universite Francaise d’Egypte (UFEID Lab), Universite Francaise d’Egypte, Cairo 11837, Egypt.

³Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt.

چکیده

This study delves into the potential polynomial and rational wave solutions of the Kudryashov-Sinelshchikov equation. This equation has multiple applications including the modeling of propagation for nonlinear waves in various physical systems. Through detailed numerical simulations using the finite element approach, we present a set of accurate solitary and soliton solutions for this equation. To validate the effectiveness of our proposed method, we utilize a collocation finite element approach based on quintic B-spline functions. Error norms, including $L_2$ and $L_8$, are employed to assess the precision of our numerical solutions, ensuring their reliability and accuracy. Visual representations, such as graphs derived from tabulated data, offer valuable insights into the dynamic changes of the equation over time or in response to varying parameters. Furthermore, we compute conservation quantities of motion and investigate the stability of our numerical scheme using Von Neumann's theory, providing a comprehensive analysis of the Kudryashov-Sinelshchikov equation and the robustness of our computational approach. The strong alignment between our analytical and numerical results underscores the efficacy of our methodology, which can be extended to tackle more complex nonlinear models with direct relevance to various fields of science and engineering.

کلیدواژه‌ها

Quintic B-spline؛ Finite element method؛ Nonlinear wave equations؛ Error estimation