Mittag-Leffler Euler Integrator for a Stochastic Fractional Order Equation with Additive Noise
Journal article, 2020

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.

Riesz kernel

Euler integrator

strong convergence

stochastic differential equations

integro-differential equations

fractional equations

Author

Mihaly Kovacs

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Stig Larsson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Fardin Saedpanah

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

SIAM Journal on Numerical Analysis

0036-1429 (ISSN) 1095-7170 (eISSN)

Vol. 58 1 66-85

Nonlocal deterministic and stochastic differential equations: analysis and numerics

Swedish Research Council (VR), 2019-01-01 -- 2021-12-31.

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Roots

Basic sciences

DOI

10.1137/18M1177895

More information

Latest update

3/16/2020