Well-posedness and Mittag-Leffler Euler integrator for space-time fractional SPDEs with fractionally integrated additive noise

  title={Well-posedness and Mittag-Leffler Euler integrator for space-time fractional SPDEs with fractionally integrated additive noise},
  author={Xinjie Dai and Jialin Hong and Derui Sheng},
This paper considers the space-time fractional stochastic partial differential equation (SPDE, for short) with fractionally integrated additive noise, which is general and includes many (fractional) SPDEs with additive noise. Firstly, the existence, uniqueness and temporal regularity of the mild solution are presented. Then the Mittag–Leffler Euler integrator is proposed as a time-stepping method to numerically solve the underlying model. Two key ingredients are developed to overcome the… 
1 Citations

Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise

. Super- and sub- diffusions are two typical types of anomalous diffusions in the nat- ural world. In this work, we discuss the numerical scheme for the model describing the competition between super-



Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation

The Euler–Maruyama method is developed for solving numerically the equation, and then its strong convergence is proven under the same conditions as the well-posedness.

Numerical approximation of stochastic time-fractional diffusion

We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a

Mittag-Leffler Euler Integrator for a Stochastic Fractional Order Equation with Additive Noise

A class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered and 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.

Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise

  • Arnulf JentzenP. Kloeden
  • Mathematics, Computer Science
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2008
A new numerical scheme for the time discretization of the finite-dimensional Galerkin stochastic differential equations is introduced, which is called the exponential Euler scheme, and it is proved that it converges faster than the classical numerical schemes for this equation with the general noise.

Galerkin finite element approximation of a stochastic semilinear fractional subdiffusion with fractionally integrated additive noise

A Galerkin finite element method is applied to approximate the solution of a semilinear stochastic space and time fractional subdiffusion problem with the Caputo fractional derivative of the order

High-Accuracy Time Discretization of Stochastic Fractional Diffusion Equation

  • Xing Liu
  • Mathematics
    Journal of Scientific Computing
  • 2021
A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise by modifying the semi-implicit Euler scheme to improve the temporal convergence rate.

Efficient simulation of nonlinear parabolic SPDEs with additive noise

Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations

A PDE Approach to Space-Time Fractional Parabolic Problems

An implicit fully-discrete scheme: first-degree tensor product finite elements in space and an implicit finite difference discretization in time is proposed and proven: stability and error estimates are proved for this scheme.