التفاصيل البيبلوغرافية
| العنوان: |
A Collocation Approach for the Nonlinear Fifth-Order KdV Equations Using Certain Shifted Horadam Polynomials. |
| المؤلفون: |
Abd-Elhameed, Waleed Mohamed1 (AUTHOR) waleed@cu.edu.eg, Alqubori, Omar Mazen2 (AUTHOR) ommohamad3@uj.edu.sa, Atta, Ahmed Gamal3 (AUTHOR) ahmed_gamal@edu.asu.edu.eg |
| المصدر: |
Mathematics (2227-7390). Jan2025, Vol. 13 Issue 2, p300. 26p. |
| مصطلحات موضوعية: |
*NONLINEAR equations, *WAVES (Physics), *POLYNOMIALS, *EQUATIONS |
| مستخلص: |
This paper proposes a numerical algorithm for the nonlinear fifth-order Korteweg–de Vries equations. This class of equations is known for its significance in modeling various complex wave phenomena in physics and engineering. The approximate solutions are expressed in terms of certain shifted Horadam polynomials. A theoretical background for these polynomials is first introduced. The derivatives of these polynomials and their operational metrics of derivatives are established to tackle the problem using the typical collocation method to transform the nonlinear fifth-order Korteweg–de Vries equation governed by its underlying conditions into a system of nonlinear algebraic equations, thereby obtaining the approximate solutions. This paper also includes a rigorous convergence analysis of the proposed shifted Horadam expansion. To validate the proposed method, we present several numerical examples illustrating its accuracy and effectiveness. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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