Work

Optimal and Computational Analysis Under the Noisy Environment in Biological Processes: The Stochastic Schnakenberg Model

Year: 2025

Type: article

Abstract: This article is concerned with the numerical approximation of the Schnakenberg model under the influence of time white noise. This model consists of nonlinear stochastic differential equations of Itô type and due to randomness, these equations are rarely solved, exactly. The Schnakenberg models are used in various fields of life such as pattern formation in skin analysis, embryogenesis, and morphogen. Schauder’s fixed point theorem is used to ensure that a solution exists. The proposed stochastic weighted average scheme and nonstandard finite difference scheme are developed to deal with the numerically underlying model. The stability of the given schemes is shown by the von Neumann criteria. The proposed stochastic Weighted Average finite difference scheme is stable for $$\lambda \ge \frac{1}{2}$$ and von Neumann stable for $$\lambda < \frac{1}{2}$$ . The proposed stochastic finite difference scheme is von Neumann stable. In the mean square sense, the consistency of the proposed schemes is proved. The 2D and 3D plots for the different values of the parameters depict the efficacy of time-efficient numerical schemes.

Source: Journal of Nonlinear Mathematical Physics

DOI: 10.1007/s44198-025-00311-7

Authors: Nauman Ahmed, Muhammad Waqas Yasin, Muhammad Sajid Iqbal, Baboucarr Ceesay, Muhammad Zafarullah Baber

Institutions: University of Lahore, University of Narowal, Liverpool John Moores University, National University of Sciences and Technology, University of the Gambia

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,490

OpenAlex ID: W4413513838