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Mathematics > Numerical Analysis

arXiv:1803.04151 (math)
[Submitted on 12 Mar 2018 (v1), last revised 16 Jan 2020 (this version, v3)]

Title:Mittag-Leffler Euler integrator for a stochastic fractional order equation with additive noise

Authors:Mihály Kovács, Stig Larsson, Fardin Saedpanah
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Abstract:Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered. A generalized exponential Euler method, named here as the Mittag-Leffler Euler integrator, is used for the temporal discretization, while the spatial discretization is performed by the spectral Galerkin method. The temporal rate of strong convergence is found to be (almost) twice compared to when the backward Euler method is used together with a convolution quadrature for time discretization. Numerical experiments that validate the theory are presented.
Comments: 20 pages, 5 figures
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1803.04151 [math.NA]
  (or arXiv:1803.04151v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1803.04151
Journal reference: SIAM J. Numer. Anal. 58 (2020), 66-85
Related DOI: https://doi.org/10.1137/18M1177895

Submission history

From: Fardin Saedpanah [view email]
[v1] Mon, 12 Mar 2018 08:32:27 UTC (49 KB)
[v2] Tue, 7 May 2019 11:15:57 UTC (41 KB)
[v3] Thu, 16 Jan 2020 09:25:16 UTC (41 KB)
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