Numerical solution for stochastic extended Fisher-Kolmogorov equation

Sweilam, N. H.; El-Sakout, D. M.; Muttardi, M. M.

doi:10.1016/j.chaos.2021.111213

Cited by 11 publications

(4 citation statements)

References 12 publications

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“…Arqub et al worked on the numerical computing of the Singular Lane-Emden type model by using the reproducing Kernal discretization method 40 . Sweilam et al worked on the numerical solution of a stochastic extended Fisher-Kolmogorov equation perturbed by multiplicative noise 41 .…”

Section: Introductionmentioning

confidence: 99%

Numerical study of diffusive fish farm system under time noise

Yasin,

Ahmed,

Saeed

et al. 2024

Sci Rep

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In the current study, the fish farm model perturbed with time white noise is numerically examined. This model contains fish and mussel populations with external food supplied. The main aim of this work is to develop time-efficient numerical schemes for such models that preserve the dynamical properties. The stochastic backward Euler (SBE) and stochastic Implicit finite difference (SIFD) schemes are designed for the computational results. In the mean square sense, both schemes are consistent with the underlying model and schemes are von Neumann stable. The underlying model has various equilibria points and all these points are successfully gained by the SIFD scheme. The SIFD scheme showed positive and convergent behavior for the given values of the parameter. As the underlying model is a population model and its solution can attain minimum value zero, so a solution that can attain value less than zero is not biologically possible. So, the numerical solution obtained by the stochastic backward Euler is negative and divergent solution and it is not a biological phenomenon that is useless in such dynamical systems. The graphical behaviors of the system show that external nutrient supply is the important factor that controls the dynamics of the given model. The three-dimensional results are drawn for the various choices of the parameters.

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Section: Introductionmentioning

confidence: 99%

Numerical study of diffusive fish farm system under time noise

Yasin,

Ahmed,

Saeed

et al. 2024

Sci Rep

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“…White-noise-driven linear elliptic and parabolic spectral power distribution functions are approximated numerically using finite element and difference approaches, which are presented, examined, and tested in [21]. Difference approximations of the integral and weak formulations of the SPDEs and finite element methods can also be found in [22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

A Reliable Computational Scheme for Stochastic Reaction–Diffusion Nonlinear Chemical Model

Arif

Abodayeh

Nawaz

2023

Axioms

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The main aim of this contribution is to construct a numerical scheme for solving stochastic time-dependent partial differential equations (PDEs). This has the advantage of solving problems with positive solutions. The scheme provides conditions for obtaining positive solutions, which the existing Euler–Maruyama method cannot do. In addition, it is more accurate than the existing stochastic non-standard finite difference (NSFD) method. Theoretically, the suggested scheme is more accurate than the current NSFD method, and its stability and consistency analysis are also shown. The scheme is applied to the linear scalar stochastic time-dependent parabolic equation and the nonlinear auto-catalytic Brusselator model. The deficiency of the NSFD in terms of accuracy is also shown by providing different graphs. Many observable occurrences in the physical world can be traced back to certain chemical concentrations. Examining and understanding the inter-diffusion between chemical concentrations is important, especially when they coincide. The Brusselator model is the gold standard for describing the relationship between chemical concentrations and other variables in chemical systems. A computational code for the proposed model scheme may be made available to readers upon request for convenience.

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“…Several numerical methods are introduced for obtaining the numerical solution of Fisher-Kolmogorov equation. In (Sweilam, ElSakout & Muttardi, 2021), authors derived a new compact finite difference scheme in the spatial direction and used the semi-implicit Euler-Maruyama approach in the temporal direction to study a stochastic extended FisherKolmogorov equation with multiplicative noise numerically. In (Kadri & Omrani, 2011), a Crank-Nicolson type finite difference scheme to approximate the nonlinear evolutionary Extended Fisher-Kolmogorov (EFK) equation is presented.…”

Section: Introductionmentioning

confidence: 99%