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Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model

  • Muhammad W. Yasin , Muhammad S. Iqbal , Aly R. Seadawy ORCID logo EMAIL logo , Muhammad Z. Baber , Muhammad Younis and Syed T. R. Rizvi
Published/Copyright: December 7, 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 2

Abstract

In this study, we give the numerical scheme to the stochastic nonlinear advection diffusion equation. This models is considered with white noise (or random process) having same intensity by changing frequencies. Furthermore, the stability and consistency of proposed scheme are also discussed. Moreover, it is concerned about the analytical solutions, the Riccati equation mapping method is adopted. The different families of single (shock and singular) and mixed (complex solitary-shock, shock-singular, and double-singular) form solutions are obtained with the different choices of free parameters. The graphical behavior of solutions is also depicted in 3D and corresponding contours.

Keywords: consistency; numerical scheme; Riccati equation mapping method; stability; stochastic nonlinear advection diffusion equation
Corresponding author: Aly R. Seadawy, Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia, E-mail: aly742001@gmail.com

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-03-17
Revised: 2021-09-04
Accepted: 2021-11-04
Published Online: 2021-12-07

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0113
Keywords for this article
consistency; numerical scheme; Riccati equation mapping method; stability; stochastic nonlinear advection diffusion equation

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  1. Frontmatter
  2. Original Research Articles
  3. Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
  4. Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
  5. Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
  6. On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
  7. On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
  8. A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
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  14. Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
  15. Investigation of nonlinear fractional delay differential equation via singular fractional operator
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  18. Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
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  22. Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics
  23. Contrasting effects of prey refuge on biodiversity of species
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