A diffusive Lotka–Volterra model with Robin boundary condition and sign-changing growth rates in time-periodic environment

Zhang, Shunqin; Zhu, Xuege; Liu, Xiaowei

doi:10.1016/j.nonrwa.2023.103856

Cited by 1 publication

(3 citation statements)

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“…The solution of the Lotka-Volterra competition system (2) can now be obtained through solving the family of discretized equations ( 9) together with Dirichlet boundary condition (10) or Neumann boundary conditions (11). Now, suppose that we have the approximate solution of ( 9) at time level k − 1 for k ≥ 1.…”

Section: The Hybrid Taylor-touchard Algorithmmentioning

confidence: 99%

“…Still, we are required to implement the boundary conditions (10) or (11) and incorporate them into the matrix Eq. (63).…”

Section: If We Rephrase the Last Equations We Have Formentioning

confidence: 99%

“…Cherniha et al [10] provided a review of up-to-date solutions for the diffusive model, presenting a wide range of exact solutions for its applications. Numerous other works on the simulation and discussion of dynamics in the diffusive model can be found in [11][12][13][14] and references therein. In this research paper, our primary focus is on the approximate solutions of a system of partial differential equations (PDEs) comprising two nonlinear equations with quadratic terms (see [15]):…”

Section: Introductionmentioning

confidence: 99%

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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: The Hybrid Taylor-touchard Algorithmmentioning

confidence: 99%

“…Still, we are required to implement the boundary conditions (10) or (11) and incorporate them into the matrix Eq. (63).…”

Section: If We Rephrase the Last Equations We Have Formentioning

confidence: 99%