Third-Kind Chebyshev Spectral Collocation Method for Solving Models of Two Interacting Biological Species

Contemporary Mathematics, Год журнала: 2024, Номер unknown, С. 6189 - 6207

Опубликована: Дек. 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.

Язык: Английский

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A Collocation Approach for the Nonlinear Fifth-Order KdV Equations Using Certain Shifted Horadam Polynomials

Mathematics, Год журнала: 2025, Номер 13(2), С. 300 - 300

Опубликована: Янв. 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.

Язык: Английский

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Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers

Axioms, Год журнала: 2025, Номер 14(4), С. 286 - 286

Опубликована: Апрель 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

Язык: Английский

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

Boundary Value Problems, Год журнала: 2025, Номер 2025(1)

Опубликована: Апрель 15, 2025

Язык: Английский

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