Accurate and efficient matrix techniques for solving the fractional Lotka–Volterra population model

Izadi, Mohammad; Yüzbaşı, Şuayip; Adel, Waleed

doi:10.1016/j.physa.2022.127558

Cited by 20 publications

(4 citation statements)

References 43 publications

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“…The applications of the spectral collocation approach with exponential-order accuracy have been examined for various model problems in physical sciences. For example, we may draw your attention to the recently published works [23][24][25][26][27][28][29][30]. The Touchard polynomials, also known as Touchard-Riordan polynomials or exponential polynomials, constitute a family of functions prominent in combinatorics and partition theory [31].…”

Section: Introductionmentioning

confidence: 99%

A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion

Izadi,

El-mesady,

Adel

2024

Mathematical Modelling and Numerical Simulation With Applications

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This paper presents the computational solutions of a time-dependent nonlinear system of partial differential equations (PDEs) known as the Lotka-Volterra competition system with diffusion. We propose a combined semi-discretized spectral matrix collocation algorithm to solve this system of PDEs. The first part of the algorithm deals with the time-marching procedure, which is performed using the well-known Taylor series formula. The resulting linear systems of ordinary differential equations (ODEs) are then solved using the spectral matrix collocation technique based on the novel Touchard family of polynomials. We discuss and establish the error analysis and convergence of the proposed method. Additionally, we examine the stability analysis and the equilibrium points of the model to determine the stability condition for the system. We perform numerical simulations using diverse model parameters and with different Dirichlet and Neumann boundary conditions to demonstrate the utility and applicability of our combined Taylor-Touchard spectral collocation algorithm.

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Section: Introductionmentioning

confidence: 99%

A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion

Izadi,

El-mesady,

Adel

2024

Mathematical Modelling and Numerical Simulation With Applications

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“…In [46], the authors defined a fractional clique collocation method for numerically solving the fractional Brusselator chemical model. In [47], the researchers derived efficient matrix techniques for solving the fractional Lotka-Volterra population model.…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Mathematical Model of Banana Xanthomonas Wilt Disease Using Caputo Derivatives

Manickam,

Kavitha,

Benevatho Jaison

et al. 2024

Contemp. Math.

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This article investigates a fractional-order mathematical model of Banana Xanthomonas Wilt disease while considering control measures using Caputo derivatives. The proposed model is numerically solved using the L1-based predictor-corrector method to explore the model’s dynamics in a particular time range. Stability and error analyses are performed to justify the efficiency of the scheme. The non-local nature of the Caputo fractional derivative, which includes memory effects in the system, is the main motivation for incorporating this derivative in the model. We obtain varieties in the model dynamics while checking various fractional order values.

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“…These methods have been successfully applied to a number of significant model problems with various (orthogonal) basis functions. Among these types of bases, we mention Morgan-Voyce [13] , Vieta-Lucas [14] , Bessel [15] , [16] , [17] , Fibonacci [18] , Jacobi [19] , Chebyshev [20] , [21] , [22] , [23] , [24] , and Vieta-Fibonacci [25] , to name a few.…”

Section: Introductionmentioning

confidence: 99%

Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods

Izadi,

Singh,

Noeiaghdam

2023

Heliyon

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Accurate and efficient matrix techniques for solving the fractional Lotka–Volterra population model

Cited by 20 publications

References 43 publications

A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion

A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion

A Fractional-Order Mathematical Model of Banana Xanthomonas Wilt Disease Using Caputo Derivatives

Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods

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