Mittag-Leffler Euler Integrator for a Stochastic Fractional Order Equation with Additive Noise
Artikel i vetenskaplig tidskrift, 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

Författare

Mihaly Kovacs

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Stig Larsson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Fardin Saedpanah

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

SIAM Journal on Numerical Analysis

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

Vol. 58 1 66-85

Icke-lokala deterministiska och stokastiska differentialekvationer: analys och numerik

Vetenskapsrådet (VR), 2019-01-01 -- 2021-12-31.

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Fundament

Grundläggande vetenskaper

DOI

10.1137/18M1177895

Mer information

Senast uppdaterat

2020-03-16