A compact Fourth-Order Implicit-Explicit Runge-Kutta Type Method for Solving Diffusive Lotka–Volterra System

Sabawi, Younis A.; Pirdawood, Mardan A.; Sadeeq, Mohammed I.

doi:10.1088/1742-6596/1999/1/012103

Cited by 9 publications

(8 citation statements)

References 16 publications

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“…A few analytical and computational strategies have been developed to deal with the model problem (2) with initial condition (3) accompanied with boundary condition (4) or (5). Let us mention the G ′ /G-expansion approach [16], the finite difference scheme [17], and the compact implicit-explicit RK type techniques [18]. To acquire the approximate solution of model ( 2) along with its conditions, we shall adopt a spectral matrix collocation algorithm based on a novel Touchard family of polynomials accompanied by the Taylor expansion technique [19][20][21][22].…”

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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“…The stability of fixed points is a critical issue in population dynamical models, with numerous mathematical models presented to explore this [4][5][6][7][8]. Furthermore, the resolution of the predator-prey relationship is another targeted area, as evidenced by several studies [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

Al-Sadi,

Al-Saif

2023

MMEP

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This study introduces a novel method aimed at deriving approximate solutions for diffusive prey-predator systems. The proposed method seeks to circumvent the limitations of extant techniques, which frequently grapple with obtaining accurate analytical solutions and managing intricate computational operations. This new approach amalgamates the Shehu transformation, Akbari-Ganji's method, and Padé Approximant to facilitate a more precise and efficient solution. The accuracy, efficiency, and effectiveness of the proposed method are assessed through the analysis of two exemplar cases in one-and two-dimensional spaces. Results gleaned from the novel method underscore its superior accuracy and efficiency compared to traditional methods used for approximating analytical solutions to similar problems. Further, the utilization of infographics and tables elucidates the significance, validity, and indispensability of the proposed approach. This research augments our comprehension of biological systems and their interactions with the environment, thereby presenting a valuable contribution to the academic discourse.

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“…In addition, we propose a method to avoid the difficulties that appear when the models of ERK cell signalling pathway transfer to stiff nonlinear equations with an implicit method. This method is called Implicit -Explicit (IMEX) schemes for more details [12][13][14][15]. Consider the numerical method of the following system of stiff ordinary differential equation:…”

Section: Introductionmentioning

confidence: 99%

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Rasool

Pirdawood

Sabawi

et al. 2022

PJBAS

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Many complex cell signalling pathways and chemical reaction networks include many variables and parameters; this is sometimes a big issue for identifying critical model elements and describing the model dynamics. Therefore, model reduction approaches can be employed as a mathematical tool to reduce the number of elements. In this study, we use a new technique for model reduction: the Lumping of parameters for the simple linear chemical reaction network and the complex cell signalling pathway that is extracellular-signal-regulated kinase (ERK) pathways. Moreover, we propose a high-order and accurate method for solving stiff nonlinear ordinary differential equations. The curtail idea of this scheme is based on splitting the problem into stiff and non-stiff terms. More specifically, stiff discretization uses the implicit method, and nonlinear discretization uses the explicit method. This is consequently leading to a reduction in the computational cost of the scheme.The main aim of this study is to reduce the complex cell signalling pathway models by proposing an accurate numerical approximation Runge-Kutta method. This improves one's understanding of such behaviour of these systems and gives an accurate approximate solution. Based on the suggested technique, the simple model's parameters are minimized from 6 to 3, and the complex models from 11 to 8. Resultsshow that there is a good agreement between the original models and the simplified models.

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A compact Fourth-Order Implicit-Explicit Runge-Kutta Type Method for Solving Diffusive Lotka–Volterra System

Cited by 9 publications

References 16 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 Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

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