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

Mohammad Izadi; Ahmed El-mesady; Waleed Adel

doi:10.53391/mmnsa.1408997

EN

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

Abstract

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.

Keywords

Collocation points, Convergent analysis, Stability, Touchard polynomials, Taylor series formula

References

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Details

Primary Language

English

Subjects

Numerical Analysis, Biological Mathematics

Journal Section

Research Article

Authors

Mohammad Izadi
0000-0002-6116-4928
Iran

Ahmed El-mesady This is me
0000-0003-2009-3905
Egypt

Waleed Adel ^*
0000-0002-0557-8536
Egypt

Publication Date

March 31, 2024

Submission Date

December 23, 2023

Acceptance Date

March 9, 2024

Published in Issue

Year 2024 Volume: 4 Number: 1

DOI

https://doi.org/10.53391/mmnsa.1408997

IZ

https://izlik.org/JA77RK52BZ

APA

Izadi, M., El-mesady, A., & Adel, W. (2024). A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion. Mathematical Modelling and Numerical Simulation With Applications, 4(1), 37-65. https://doi.org/10.53391/mmnsa.1408997

AMA

1.Izadi M, El-mesady A, Adel W. A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion. MMNSA. 2024;4(1):37-65. doi:10.53391/mmnsa.1408997

Chicago

Izadi, Mohammad, Ahmed El-mesady, and Waleed Adel. 2024. “A Novel Touchard Polynomial-Based Spectral Matrix Collocation Method for Solving the Lotka-Volterra Competition System With Diffusion”. Mathematical Modelling and Numerical Simulation With Applications 4 (1): 37-65. https://doi.org/10.53391/mmnsa.1408997.

EndNote

Izadi M, El-mesady A, Adel W (March 1, 2024) A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion. Mathematical Modelling and Numerical Simulation with Applications 4 1 37–65.

IEEE

[1]M. Izadi, A. El-mesady, and W. Adel, “A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion”, MMNSA, vol. 4, no. 1, pp. 37–65, Mar. 2024, doi: 10.53391/mmnsa.1408997.

ISNAD

Izadi, Mohammad - El-mesady, Ahmed - Adel, Waleed. “A Novel Touchard Polynomial-Based Spectral Matrix Collocation Method for Solving the Lotka-Volterra Competition System With Diffusion”. Mathematical Modelling and Numerical Simulation with Applications 4/1 (March 1, 2024): 37-65. https://doi.org/10.53391/mmnsa.1408997.

JAMA

1.Izadi M, El-mesady A, Adel W. A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion. MMNSA. 2024;4:37–65.

MLA

Izadi, Mohammad, et al. “A Novel Touchard Polynomial-Based Spectral Matrix Collocation Method for Solving the Lotka-Volterra Competition System With Diffusion”. Mathematical Modelling and Numerical Simulation With Applications, vol. 4, no. 1, Mar. 2024, pp. 37-65, doi:10.53391/mmnsa.1408997.

Vancouver

1.Mohammad Izadi, Ahmed El-mesady, Waleed Adel. A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion. MMNSA. 2024 Mar. 1;4(1):37-65. doi:10.53391/mmnsa.1408997

Math Model Numer Simul Appl - 2025

The published articles in MMNSA are licensed under a Creative Commons Attribution 4.0 International License

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

Abstract

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

Abstract

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References

Details

Primary Language

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Journal Section

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