Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise
Affiliation
Lvliang University; University of Chester; King Fahd University of Petroleum and MineralsPublication Date
2023-09-03
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Recently, Kovács et al. considered a Mittag‐Leffler Euler integrator for a stochastic semilinear Volterra integral‐differential equation with additive noise and proved the strong convergence error estimates [see SIAM J. Numer. Anal. 58(1) 2020, pp. 66‐85]. In this article, we shall consider the Mittag‐Leffler integrators for more general models: stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise. The mild solutions of our models involve four different Mittag‐Leffler functions. We first consider the existence, uniqueness and the regularities of the solutions. We then introduce the full discretization schemes for solving the problems. The temporal discretization is based on the Mittag‐Leffler integrators and the spatial discretization is based on the spectral method. The optimal strong convergence error estimates are proved under the reasonable assumptions for the semilinear term and for the regularity of the noise. Numerical examples are given to show that the numerical results are consistent with the theoretical results.Citation
Hu, Y., Yan, Y., & Sarwar, S. (2023). Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise. Numerical Methods for Partial Differential Equations, vol(issue), pages. https://doi.org/10.1002/num.23068Publisher
WileyAdditional Links
https://onlinelibrary.wiley.com/doi/full/10.1002/num.23068Type
articleDescription
This article is not available on ChesterRepISSN
0749-159XEISSN
1098-2426ae974a485f413a2113503eed53cd6c53
10.1002/num.23068