Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations

Mourad S. Semary; M. T. M. Elbarawy; Aisha F. Fareed; Mourad S. Semary; M. T. M. Elbarawy; Aisha F. Fareed

doi:10.3934/math.2022283

AIMS Mathematics

2022, Volume 7, Issue 4: 5093-5105. doi: 10.3934/math.2022283

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Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations

1.
Department of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, Benha, Egypt
2.
Engineering Mathematics and Physics Dept., Faculty of Engineering, Fayoum University, Fayoum, Egypt

Received: 19 October 2021 Revised: 06 December 2021 Accepted: 12 December 2021 Published: 30 December 2021

In this paper, a numerical method to solve a class of stochastic nonlinear differential equations is introduced. The proposed method is based on the Temimi-Ansari method. The special states of the four systems are studied to show that the proposed method is efficient and applicable. These systems are stochastic Langevin's equation, Ginzburg-Landau equation, Davis-Skodje, and Brusselator systems. The results clarify the accuracy and efficacy of the presented new method with no need for any restrictive assumptions for nonlinear terms.
- Temimi-Ansari method,
- stochastic nonlinear differential equations,
- Langevin's equation,
- Ginzburg-Landau equation,
- Davis-Skodje and Brusselator systems
Citation: Mourad S. Semary, M. T. M. Elbarawy, Aisha F. Fareed. Discrete Temimi-Ansari method for solving a class of stochastic nonlinear differential equations[J]. AIMS Mathematics, 2022, 7(4): 5093-5105. doi: 10.3934/math.2022283

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Abstract

In this paper, a numerical method to solve a class of stochastic nonlinear differential equations is introduced. The proposed method is based on the Temimi-Ansari method. The special states of the four systems are studied to show that the proposed method is efficient and applicable. These systems are stochastic Langevin's equation, Ginzburg-Landau equation, Davis-Skodje, and Brusselator systems. The results clarify the accuracy and efficacy of the presented new method with no need for any restrictive assumptions for nonlinear terms.

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