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Global Analysis and Discrete Mathematics، جلد ۸، شماره ۲، صفحات ۳۷-۶۷
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عنوان انگلیسی Upwind Implicit Scheme for the Numerical Solution of Stochastic Advection–Diffusion Partial Differential Equations
چکیده انگلیسی مقاله Stochastic partial differential equations (SPDEs) are significant in various fields such as epidemiology, mechanics, microelectronics, chemistry, and finance. Obtaining analytical solutions for SPDEs is either difficult or impossible; therefore, researchers are very interested in effective numerical methods for studying the behavior of these equations. In this paper, we introduce a stochastic finite difference (SFD) scheme for the numerical solution of the It^{o} stochastic advection--diffusion equation. We discuss the consistency, stability, and convergence of the scheme, and we also determine its order of convergence. Finally, to validate the effectiveness and accuracy of the SFD scheme, we analyze the numerical results and compare them with those from existing SFD schemes.
کلیدواژه‌های انگلیسی مقاله Ito stochastic partial differential equation,Finite difference,Consistency,stability,Convergence
نویسندگان مقاله Mehran Namjoo |
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Mehran Aminian |
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Ali Mohebbian |
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Mehdi Karami |
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

Hossein Salmei |
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

نشانی اینترنتی https://ansne.du.ac.ir/article_434_4aebd5bb2c291ac1126142ad813f2fb1.pdf
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