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Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise
Yan, Yubin Hu, Ye Sarwar, Shahzad
Yan, Yubin
Hu, Ye
Sarwar, Shahzad
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2023-09-03
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Abstract
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. (2024). Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise. Numerical Methods for Partial Differential Equations, 40(2), e23068. https://doi.org/10.1002/num.23068
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Wiley
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Numerical Methods for Partial Differential Equations
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DOI
10.1002/num.23068
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Article
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This is the peer reviewed version of the following article: [Hu, Y., Yan, Y., & Sarwar, S. (2024). Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise. Numerical Methods for Partial Differential Equations, 40(2), e23068], which has been published in final form at [https://doi.org/10.1002/num.23068]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
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ISSN
0749-159X
EISSN
1098-2426