An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise
Name:
Publisher version
View Source
Access full-text PDFOpen Access
View Source
Check access options
Check access options
Affiliation
University of Chester, Lvliang University, Jimei UniversityPublication Date
2020-06-02
Metadata
Show full item recordOther Titles
An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noiseAbstract
We consider the strong convergence of the numerical methods for solving stochastic subdiffusion problem driven by an integrated space-time white noise. The time fractional derivative is approximated by using the L1 scheme and the time fractional integral is approximated with the Lubich's first order convolution quadrature formula. We use the Euler method to approximate the noise in time and use the truncated series to approximate the noise in space. The spatial variable is discretized by using the linear finite element method. Applying the idea in Gunzburger \et (Math. Comp. 88(2019), pp. 1715-1741), we express the approximate solutions of the fully discrete scheme by the convolution of the piecewise constant function and the inverse Laplace transform of the resolvent related function. Based on such convolution expressions of the approximate solutions, we obtain the optimal convergence orders of the fully discrete scheme in spatial multi-dimensional cases by using the Laplace transform method and the corresponding resolvent estimates.Citation
Wu, X., Yan, Y., & Yan, Y. (2020). An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise. Applied Numerical Mathematics, 157, 67-87.Publisher
ElsevierJournal
Applied Numerical MathematicsType
ArticleEISSN
0168-9274ae974a485f413a2113503eed53cd6c53
10.1016/j.apnum.2020.05.014
Scopus Count
Collections
Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by/4.0/