Fractional stochastic Burgers-Type Equation in H\"older space -wellposedness and approximations-

TL;DR

This paper establishes the well-posedness and convergence rates of spectral Galerkin and exponential-Euler discretizations for a fractional stochastic Burgers-type equation in H"older space, advancing numerical analysis of such SPDEs.

Contribution

It proves existence and uniqueness of solutions and provides convergence rates for combined spectral Galerkin and exponential-Euler approximation schemes.

Findings

Existence of a pathwise unique mild solution in H"older space.

Derived convergence rates for Galerkin and discretization schemes.

Validated the effectiveness of combined spectral and exponential-Euler methods.

Abstract

In this work, we use the spectral Galerkin method to prove the existence of a pathwise unique mild solution of a fractional stochastic partial differential equation of Burgers type in a H\"older space. We get the temporal regularity and using a combination of Galerkin and exponential-Euler methods, we obtain a fully discretization scheme of the solution. Moreover, we calculate the rates of convergence for both approximations (Galerkin and fully discretization) with respect to time and to space.