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

Document Type : Research Article

Authors

• H. Samy ¹
• W. Adel ^{2, 3}
• I. Hanafy ¹
• M. Ramadan ¹

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

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

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

10.22067/ijnao.2024.87548.1422

Abstract

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 L2 and L∞, 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 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. 

Keywords

• Quintic B-spline
• Finite element method
• Error analysis

Main Subjects

• Numerical methods for differential equations and its applications

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