Research PaperNo Access

Comparative analysis of numerical and newly constructed soliton solutions of stochastic Fisher-type equations in a sufficiently long habitat

Muhammad Z. Baber

Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

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Aly R. Seadway

Mathematics Department, Faculty of science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

E-mail Address: aabdelalim@taibahu.edu.sa

Corresponding author.

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Muhammad S. Iqbal

Department of Humanities & Basic Science, Military College of Signals, NUST, Islamabad, Pakistan

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Nauman Ahmed

Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

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Muhammad W. Yasin

Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

Department of Mathematics, University of Narowal, Narowal, Pakistan

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, and

Muhammad O. Ahmed

Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan

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https://doi.org/10.1142/S0217979223501552Cited by:17 (Source: Crossref)

Abstract

This paper is a key contribution with respect to the applications of solitary wave solutions to the unique solution in the presence of the auxiliary data. Hence, this study provides an insight for the unique selection of solitons for the physical problems. Additionally, the novel numerical scheme is developed to compare the result. Further, this paper deals with the stochastic Fisher-type equation numerically and analytically with a time noise process. The nonstandard finite difference scheme of stochastic Fisher-type equation is proposed. The stability analysis and consistency of this proposed scheme are constructed with the help of Von Neumann analysis and Itô integral. This model is applicable in the wave proliferation of a viral mutant in an infinitely long habitat. Additionally, for the sake of exact solutions, we used the Riccati equation mapping method. The solutions are constructed in the form of hyperbolic, trigonometric and rational forms with the help of Mathematica 11.1. Lastly, the graphical comparisons of numerical solutions with exact wave solution with the help of Neumann boundary conditions are constructed successfully in the form of 3D and line graphs by using different values of parameters.

Keywords:

PACS: 02.20.Sv, 02.30.Jr, 11.30.−i, 47.20.Ky

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