Mittag--Leffler Euler Integrator for a Stochastic Fractional Order Equation with Additive Noise
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 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.
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© 2020, Society for Industrial and Applied Mathematics.
History
Submitted: 28 March 2018
Accepted: 4 November 2019
Published online: 7 January 2020
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NordForsk https://doi.org/10.13039/501100004785 : 74756
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