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Application of Quintic B-Spline Finite Element Method to the Gardner-Extended KdV Equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 شهریور 1405 اصل مقاله (2 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70009.3476 | ||
| نویسندگان | ||
| Moutaz Ramadan* 1؛ Hayah Samy2 | ||
| 11. Department of Mathematics, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia. 2. Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt. | ||
| 2Basic Sciences Department, Higher Institute for Engineering and Technology at Manzala, Egypt. | ||
| چکیده | ||
| This study presents a numerical investigation of the Gardner-Extended Korteweg–de Vries (G-EKdV) equation, a fundamental nonlinear dispersive partial differential equation that effectively models solitary wave phenomena. The main objective is to accurately capture the dynamics of solitary waves and their interactions through advanced numerical simulations. The Crank-Nicholson approach is employed for time integration, while a quintic B-spline finite element method (FEM) integrated within a Galerkin framework is utilized for spatial discretization. With reliability and stability in the calculated results, this combination effectively handles the nonlinear and dispersive features of the G-EKdV equation. The numerical experiments include single solitary wave propagation and two solitons interactions. Accuracy and conservation are evaluated using error norms and invariants. Graphical representations of data points offer insightful insights into the equation's behavior over time or in response to various variables. The alignment between analytical and numerical results is crucial for validating the accuracy and reliability of the approach. This validation is essential to establish the credibility and trustworthiness of the findings. The Gardner-Extended KdV equation plays a pivotal role in modeling energy transfer mechanisms across various physical systems. The solitary wave solutions derived from this equation offer accurate representations of nonlinear wave dynamics, including marine and renewable energy technologies, plasma physics, and optical communications. | ||
| کلیدواژهها | ||
| Numerical analysis؛ Galerkin’s finite element method؛ Gardner-Extended KdV equation؛ Quintic B-spline | ||
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