کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4625936 | 1631777 | 2016 | 20 صفحه PDF | دانلود رایگان |
The Fokker–Planck equations for stochastic dynamical systems, with non-Gaussian α-stable symmetric Lévy motions, have a nonlocal or fractional Laplacian term. This nonlocality is the manifestation of the effect of non-Gaussian fluctuations. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker–Planck equations on either a bounded or infinite domain. Under a specified condition, the scheme is shown to satisfy a discrete maximum principle and to be convergent. It is validated against a known exact solution and the numerical solutions obtained by using other methods. The numerical results for two prototypical stochastic systems, the Ornstein–Uhlenbeck system and the double-well system are shown.
Journal: Applied Mathematics and Computation - Volume 278, 31 March 2016, Pages 1–20