Numerical approximations of stochastic Gray-Scott model with two novel schemes

Wang, Xiaoming; Yasin, Muhammad W.; Ahmed, Nauman; Rafiq, Muhammad; Abbas, Muhammad

doi:10.3934/math.2023257

Cited by 13 publications

(3 citation statements)

References 38 publications

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“…Here, we use the conditional expectation (conditioned by the filtration generated by Wiener process), and E(e 2νβ(t) ) is identity element; for more detail, see [30][31][32]. So, Equation (12) takes the form…”

Section: Soliton Solutions For K-o System With Stratonovich Sensementioning

confidence: 99%

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On the Soliton Solutions for the Stochastic Konno–Oono System in Magnetic Field with the Presence of Noise

et al. 2023

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In this study, we consider the stochastic Konno–Oono system to investigate the soliton solutions under the multiplicative sense. The multiplicative noise is considered firstly in the Stratonovich sense and secondly in the Ito^ sense. Applications of the Konno–Oono system include current-fed strings interacting with an external magnetic field. The F-expansion method is used to find the different types of soliton solutions in the form of dark, singular, complex dark, combo, solitary, periodic, mixed periodic, and rational functions. These solutions are applicable in the magnetic field when we study it at the micro level. Additionally, the absolute, real, and imaginary physical representations in three dimensions and the corresponding contour plots of some solutions are drawn in the sense of noise by the different choices of parameters.

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Section: Soliton Solutions For K-o System With Stratonovich Sensementioning

confidence: 99%

“…So, stochastic models are more suitable as compared to classical models. Different researchers are working on the solutions of stochastic partial differential equation [12][13][14]. In this study, we consider the stochastic coupled Konno-Oono (K-O) system in the form [15] φ xt − 2φψ = νF(φ),…”

Section: Introductionmentioning

confidence: 99%

On the Soliton Solutions for the Stochastic Konno–Oono System in Magnetic Field with the Presence of Noise

et al. 2023

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“…The dynamics of stochastic partial differential equations are the subject of many recent investigations. The authors performed in-depth analyses of several physical phenomena using the finite difference scheme [39][40][41]. Macas-Daz et al [42] studied the stochastic epidemiology model using a non-traditional finite difference approach.…”

Section: Introductionmentioning

confidence: 99%

Modelling Infectious Disease Dynamics: A Robust Computational Approach for Stochastic SIRS with Partial Immunity and an Incidence Rate

Baazeem,

Nawaz,

Arif

et al. 2023

Mathematics

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For decades, understanding the dynamics of infectious diseases and halting their spread has been a major focus of mathematical modelling and epidemiology. The stochastic SIRS (susceptible–infectious–recovered–susceptible) reaction–diffusion model is a complicated but crucial computational scheme due to the combination of partial immunity and an incidence rate. Considering the randomness of individual interactions and the spread of illnesses via space, this model is a powerful instrument for studying the spread and evolution of infectious diseases in populations with different immunity levels. A stochastic explicit finite difference scheme is proposed for solving stochastic partial differential equations. The scheme is comprised of predictor–corrector stages. The stability and consistency in the mean square sense are also provided. The scheme is applied to diffusive epidemic models with incidence rates and partial immunity. The proposed scheme with space’s second-order central difference formula solves deterministic and stochastic models. The effect of transmission rate and coefficient of partial immunity on susceptible, infected, and recovered people are also deliberated. The deterministic model is also solved by the existing Euler and non-standard finite difference methods, and it is found that the proposed scheme forms better than the existing non-standard finite difference method. Providing insights into disease dynamics, control tactics, and the influence of immunity, the computational framework for the stochastic SIRS reaction–diffusion model with partial immunity and an incidence rate has broad applications in epidemiology. Public health and disease control ultimately benefit from its application to the study and management of infectious illnesses in various settings.

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Conformable bilinear neural network method: a novel method for time-fractional nonlinear partial differential equations in the sense of conformable derivative

Ye,

Fan,

et al. 2024

Nonlinear Dyn

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Numerical approximations of stochastic Gray-Scott model with two novel schemes

Cited by 13 publications

References 38 publications

On the Soliton Solutions for the Stochastic Konno–Oono System in Magnetic Field with the Presence of Noise

On the Soliton Solutions for the Stochastic Konno–Oono System in Magnetic Field with the Presence of Noise

Modelling Infectious Disease Dynamics: A Robust Computational Approach for Stochastic SIRS with Partial Immunity and an Incidence Rate

Conformable bilinear neural network method: a novel method for time-fractional nonlinear partial differential equations in the sense of conformable derivative

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