Numerical solutions for nonlinear ordinary and fractional Newell–Whitehead–Segel equation using shifted Schröder polynomials DOI Creative Commons

N. M. Yassin,

Ahmed Gamal Atta, Emad H. Aly

et al.

Boundary Value Problems, Journal Year: 2025, Volume and Issue: 2025(1)

Published: April 15, 2025

Language: Английский

A Collocation Approach for the Nonlinear Fifth-Order KdV Equations Using Certain Shifted Horadam Polynomials DOI Creative Commons
W. M. Abd‐Elhameed, Omar Mazen Alqubori, Ahmed Gamal Atta

et al.

Mathematics, Journal Year: 2025, Volume and Issue: 13(2), P. 300 - 300

Published: Jan. 17, 2025

This paper proposes a numerical algorithm for the nonlinear fifth-order Korteweg–de Vries equations. class of equations is known its significance in modeling various complex wave phenomena physics and engineering. The approximate solutions are expressed terms certain shifted Horadam polynomials. A theoretical background these polynomials first introduced. derivatives their operational metrics established to tackle problem using typical collocation method transform equation governed by underlying conditions into system algebraic equations, thereby obtaining solutions. also includes rigorous convergence analysis proposed expansion. To validate method, we present several examples illustrating accuracy effectiveness.

Language: Английский

Citations

1
Third-Kind Chebyshev Spectral Collocation Method for Solving Models of Two Interacting Biological Species DOI Creative Commons
Mostafa Ahmed Taema, Y. H. Youssri

Contemporary Mathematics, Journal Year: 2024, Volume and Issue: unknown, P. 6189 - 6207

Published: Dec. 16, 2024

This paper develops numerical methods for solving a system of two nonlinear integro-differential equations that arise in biological modeling. A spectral collocation method utilizing third-kind Chebyshev polynomials forms the basis solution methodology, which efficiently converts into collection algebraic equations. To guarantee precise and effective calculation, these are subsequently numerically solved using Newton’s method. In comparison to current methods, suggested approach offers notable gains computational efficiency precision. The method’s accuracy is confirmed by contrasting outcomes with those derived from other published literature. further illustrate applicability, dependability, resolving complicated systems, number illustrative instances provided. ability techniques based on solve variety scientific engineering applications highlighted this work.

Language: Английский

Citations

6
Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers DOI Creative Commons
W. M. Abd‐Elhameed, Omar Mazen Alqubori,

Abdulrahim A. Alluhaybi

et al.

Axioms, Journal Year: 2025, Volume and Issue: 14(4), P. 286 - 286

Published: April 11, 2025

This article introduces new polynomials that extend the standard Leonardo numbers, generalizing Fibonacci and Lucas polynomials. A power form representation is developed for these polynomials, which crucial deriving further formulas. also presents two connection formulas linking generalized to as well several identities involving some specific numbers. Additionally, product with are provided, along computations of definite integrals based on derived

Language: Английский

Citations

0
Numerical solutions for nonlinear ordinary and fractional Newell–Whitehead–Segel equation using shifted Schröder polynomials DOI Creative Commons

N. M. Yassin,

Ahmed Gamal Atta, Emad H. Aly

et al.

Boundary Value Problems, Journal Year: 2025, Volume and Issue: 2025(1)

Published: April 15, 2025

Language: Английский

Citations

0