On the numerical solution of Fisher’s equation with coefficient of diffusion term much smaller than coefficient of reaction term

Agbavon, Koffi Messan; Appadu, Appanah Rao; Khumalo, M.

doi:10.1186/s13662-019-2080-x

Cited by 26 publications

(29 citation statements)

References 33 publications

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“…From these figures, we see that the NSFD scheme is efficient as well as the SFD scheme. Tables 3 and 4 represent the L ∞ and L 2 -errors of the exact finite difference methods, IMPEXFDI (18), IMPEXFDII (21), IMPEXFDIII (24), EXPEXFDI (27), EXPEXFDII (30), EXPEXFDIII (33). If we select the step size h = 0.5 with different time steps t, the exact schemes are reduced to the NSFD scheme [39].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…the implicit exact finite difference schemes are given by (18), (21) and (24) and the explicit exact finite difference schemes are given by (27), (30) and (33). The temporal step size satisfies t = 10h and the step size functions satisfy Ψ 1 = e h -1, Ψ 2 = 1e -h , Φ 1 = 1e -0.1 t 0.1 , Φ 2 = e 0.1 t -1 0.1 .…”

Section: Theorem 1 For the Generalized Kdv-burgersmentioning

confidence: 99%

“…In [20] Chapwanya et al designed several dynamically consistent NSFD schemes for some reaction-diffusion equations, advection-reaction equations and advection-reaction-diffusion equations by using the exact scheme of the Michaelis-Menten ordinary differential equation. Agbavon et al [21] proposed four schemes, namely FTCS-, NSFD-, FTCS with artificial viscosity and NSFD with artificial viscosity. In [22] the authors presented numerical solutions of the FitzHugh-Naguma system of equations.…”

Section: Introductionmentioning

confidence: 99%

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Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Köroğlu

2020

Adv Differ Equ

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We consider the generalized KdV-Burgers KdVB(p, m, q) equation. We have designed exact and consistent nonstandard finite difference schemes (NSFD) for the numerical solution of the KdVB(2, 1, 2) equation. In particular, we have proposed three explicit and three fully implicit exact finite difference schemes. The proposed NSFD scheme is linearly implicit. The chosen numerical experiment consists of tanh function. The NSFD scheme is compared with a standard finite difference(SFD) scheme. Numerical results show that the NSFD scheme is accurate and efficient in the numerical simulation of the kink-wave solution of the KdVB(2, 1, 2) equation. We see that while the SFD scheme yields numerical instability for large step sizes, the NSFD scheme provides reliable results for long time integration. Local truncation error reveals that the NSFD scheme is consistent with the KdVB(2, 1, 2) equation.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Theorem 1 For the Generalized Kdv-burgersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Köroğlu

2020

Adv Differ Equ

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“…In this section, we prove the positivity of the solutions and boundedness given the initial conditions 3and find the steady states of the model (2). Some methods in mathematical biology have also been used to describe properties of solutions (see [24][25][26][27] for a detailed discussion on methods for positivity of 80 solutions, boundedness and preservation of steady states).…”

Section: Model Properties and Analysismentioning

confidence: 99%

Modelling the Potential Role of Media Campaigns on the Control of Listeriosis

Chukwu

Nyabadza

2020

Preprint

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The human Listeria infection is a food-borne disease caused by the consumption of contaminated food products by the bacterial pathogen, Listeria. In this paper, we propose a mathematical model to analyze the impact of media campaigns on the spread and control of Listeriosis. The model exhibited three equilibria namely; disease-free, Listeria-free and endemic equilibria. The food contamination constant (ℛf) is determined and the local stability analyses of the model discussed. Sensitivity analysis is done to determine the model parameters that most affect the severity of the disease. Numerical simulations were carried out to assess the role of media campaigns on the Listeriosis spread. The results show that; an increase in the intensity of the media awareness campaigns, the removal rate of contaminated food products, a decrease in the contact rate of Listeria by humans results in fewer humans getting infected, thus leading to the disease eradication. An increase in the depletion of media awareness campaigns results in more humans being infected with Listeriosis. These findings may significantly impact policy and decision making in the control of Listeriosis disease.

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“…Very recently, Agbavon et al studied the Fisher's equation numerically by taking the diffusion term to be smaller than the reaction term, Mickens and Oyedeji presented travelling wave solutions to the modified Burgers and diffusionless Fisher's equations, and so on. See References .…”

Section: Introductionmentioning

confidence: 99%

Exact solutions to the family of Fisher's reaction‐diffusion equation using Elzaki homotopy transformation perturbation method

Loyinmi

Akinfe

2020

Engineering Reports

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In this research work, we propose an unprecedented hybrid algorithm which involves the coupling of a new integral transform, namely, the Elzaki transform and the well‐known homotopy perturbation method called the Elzaki homotopy transformation perturbation method (EHTPM) to solve for the exact solution of three distinct types of Fisher's equation, namely, the Fisher's equation of two cases, the sixth‐order Fisher's equation and the nonlinear diffusion equation of the Fisher type. These equations are prominent in mathematical biology and highly applicable in genetic propagation, population dynamics, stochastic processes, combustion theory, as well as a prototype model for a spreading flame, and so on. The efficacy and authenticity of this method was established via convergence and error analysis, and shows that the solutions obtained from EHTPM are unique and convergent. The results of EHTPM when compared with the exact results, homotopy results, and results from the other existing literature via table of comparison, 3D plots, and the convergence plots validates that EHTPM is an efficient and reliable tool of providing exact solutions to a wider class of nonlinear partial differential equations in a simple and straightforward manner, with no discretization, linearization, computation of Adomian polynomials, and devoid of errors.

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On the numerical solution of Fisher’s equation with coefficient of diffusion term much smaller than coefficient of reaction term

Cited by 26 publications

References 33 publications

Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Modelling the Potential Role of Media Campaigns on the Control of Listeriosis

Exact solutions to the family of Fisher's reaction‐diffusion equation using Elzaki homotopy transformation perturbation method

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