Volume 3, Issue 2 (12-2022)                   MACO 2022, 3(2): 105-118 | Back to browse issues page

‎ 10.22034/maco.3.2.10
‎ 20.1001.1.27170624.2022.3.2.10.4

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Lotfi M. Legendre spectral element and backward Euler methods for solving a family of stochastic partial differential equations. MACO 2022; 3 (2) : 10
URL: http://maco.lu.ac.ir/article-1-122-en.html
Legendre spectral element and backward Euler methods for solving a family of stochastic partial differential equations
Mahmoud Lotfi *
Abstract:   (734 Views)
In this paper, we use the spectral element method for solving the stochastic partial differential equation. For spatial discretization, we use the Legendre spectral element method, and we obtain the semi-discrete form. To solve the problem, we need to obtain the complete discrete form and we use the backward Euler method to this aim. The Weiner process is approximated by Fourier series and we obtain the fully discrete scheme of the problem. Error and convergence analysis are presented and, with a numerical example, we demonstrate the efficiency of the proposed method.
Article number: 10
Keywords: Stochastic partial differential equation, spectral element method, Legendre polynomials
Full-Text [PDF 178 kb]   (628 Downloads)    
Type of Study: Research Article | Subject: Applied Mathematics
Published: 2023/07/27
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