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A Petrov-Galerkin finite element method using polyfractonomials to solve stochastic fractional differential equations

Abedini, N ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1016/j.apnum.2021.05.031
  3. Publisher: Elsevier B.V , 2021
  4. Abstract:
  5. In this paper, we are concerned with existence, uniqueness and numerical approximation of the solution process to an initial value problem for stochastic fractional differential equation of Riemann-Liouville type. We propose and analyze a Petrov-Galerkin finite element method based on fractional (non-polynomial) Jacobi polyfractonomials as basis and test functions. Error estimates in L2 norm are derived and numerical experiments are provided to validate the theoretical results. As an illustrative application, we generate sample paths of the Riemann-Liouville fractional Brownian motion which is of importance in many applications ranging from geophysics to traffic flow in telecommunication networks. © 2021 IMACS
  6. Keywords:
  7. Brownian movement ; Finite element method ; Initial value problems ; Polynomials ; Stochastic systems ; Existence uniqueness ; Fractional differential equations ; Galerkin finite element methods ; Liouville ; Petrov Galerkin finite elements ; Petrov-Galerkin methods ; Polyfractonomial ; Riemann-liouville fractional brownian motion ; Stochastic fractional differential equation ; Stochastics ; Galerkin methods
  8. Source: Applied Numerical Mathematics ; Volume 169 , 2021 , Pages 64-86 ; 01689274 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0168927421001689