Zhu, Bi-Yun; Xiao, Ai-Guo; Li, Xue-Yang An efficient numerical method on modified space-time sparse grid for time-fractional diffusion equation with nonsmooth data. (English) Zbl 07780858 Numer. Algorithms 94, No. 4, 1561-1596 (2023). MSC: 65M70 65M06 65N35 65T40 35B65 26A33 35R11 PDFBibTeX XMLCite \textit{B.-Y. Zhu} et al., Numer. Algorithms 94, No. 4, 1561--1596 (2023; Zbl 07780858) Full Text: DOI
Cao, Jiliang; Xiao, Aiguo; Bu, Weiping A fast Alikhanov algorithm with general nonuniform time steps for a two-dimensional distributed-order time-space fractional advection-dispersion equation. (English) Zbl 07777339 Numer. Methods Partial Differ. Equations 39, No. 4, 2885-2908 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{J. Cao} et al., Numer. Methods Partial Differ. Equations 39, No. 4, 2885--2908 (2023; Zbl 07777339) Full Text: DOI
Zhang, Biao; Bu, Weiping; Xiao, Aiguo Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition. (English) Zbl 1512.65185 Numer. Algorithms 88, No. 4, 1965-1988 (2021). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{B. Zhang} et al., Numer. Algorithms 88, No. 4, 1965--1988 (2021; Zbl 1512.65185) Full Text: DOI
Wang, Junjie; Xiao, Aiguo; Bu, Weiping Spectral collocation method for a class of fractional diffusion differential equations with nonsmooth solutions. (English) Zbl 1495.65183 Math. Methods Appl. Sci. 44, No. 4, 2892-2913 (2021). Reviewer: Anouar Ben Mabrouk (Monastir) MSC: 65M70 65D05 65M12 65L60 33C45 26A33 35R11 PDFBibTeX XMLCite \textit{J. Wang} et al., Math. Methods Appl. Sci. 44, No. 4, 2892--2913 (2021; Zbl 1495.65183) Full Text: DOI
Yang, Yin; Li, Xueyang; Xiao, Aiguo Fourier pseudospectral method for fractional stationary Schrödinger equation. (English) Zbl 1468.35189 Appl. Numer. Math. 165, 137-151 (2021). MSC: 35Q55 35Q40 65M06 65T50 35R11 PDFBibTeX XMLCite \textit{Y. Yang} et al., Appl. Numer. Math. 165, 137--151 (2021; Zbl 1468.35189) Full Text: DOI
Dai, Xinjie; Xiao, Aiguo A note on Euler method for the overdamped generalized Langevin equation with fractional noise. (English) Zbl 1450.65002 Appl. Math. Lett. 111, Article ID 106669, 6 p. (2021). MSC: 65C30 65R20 35R11 60G22 60H15 PDFBibTeX XMLCite \textit{X. Dai} and \textit{A. Xiao}, Appl. Math. Lett. 111, Article ID 106669, 6 p. (2021; Zbl 1450.65002) Full Text: DOI
Zeng, Wei; Xiao, Aiguo; Bu, Weiping; Wang, Junjie; Li, Shucun A space-time Petrov-Galerkin spectral method for time fractional Fokker-Planck equation with nonsmooth solution. (English) Zbl 1462.35451 East Asian J. Appl. Math. 10, No. 1, 89-105 (2020). MSC: 35R11 35Q84 65M70 65M60 65M12 PDFBibTeX XMLCite \textit{W. Zeng} et al., East Asian J. Appl. Math. 10, No. 1, 89--105 (2020; Zbl 1462.35451) Full Text: DOI
Cao, Jiliang; Xiao, Aiguo; Bu, Weiping Finite difference/finite element method for tempered time fractional advection-dispersion equation with fast evaluation of Caputo derivative. (English) Zbl 1453.65311 J. Sci. Comput. 83, No. 3, Paper No. 48, 29 p. (2020). MSC: 65M60 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{J. Cao} et al., J. Sci. Comput. 83, No. 3, Paper No. 48, 29 p. (2020; Zbl 1453.65311) Full Text: DOI
Bu, Weiping; Shu, Shi; Yue, Xiaoqiang; Xiao, Aiguo; Zeng, Wei Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain. (English) Zbl 1442.65252 Comput. Math. Appl. 78, No. 5, 1367-1379 (2019). MSC: 65M60 65M12 65M15 35R11 PDFBibTeX XMLCite \textit{W. Bu} et al., Comput. Math. Appl. 78, No. 5, 1367--1379 (2019; Zbl 1442.65252) Full Text: DOI
Xiao, Aiguo; Wang, Junjie Symplectic scheme for the Schrödinger equation with fractional Laplacian. (English) Zbl 1423.81070 Appl. Numer. Math. 146, 469-487 (2019). MSC: 81Q05 34L40 34A08 39A12 53D05 34K28 PDFBibTeX XMLCite \textit{A. Xiao} and \textit{J. Wang}, Appl. Numer. Math. 146, 469--487 (2019; Zbl 1423.81070) Full Text: DOI
Bu, Weiping; Xiao, Aiguo An \(h\)-\(p\) version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functions. (English) Zbl 1435.65194 Numer. Algorithms 81, No. 2, 529-545 (2019). MSC: 65N30 35R11 26A33 35A01 35A02 PDFBibTeX XMLCite \textit{W. Bu} and \textit{A. Xiao}, Numer. Algorithms 81, No. 2, 529--545 (2019; Zbl 1435.65194) Full Text: DOI
Zeng, Wei; Xiao, Aiguo; Li, Xueyang Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg-Landau equations. (English) Zbl 1414.65026 Appl. Math. Lett. 93, 40-45 (2019). MSC: 65M70 65M15 35Q56 35R11 PDFBibTeX XMLCite \textit{W. Zeng} et al., Appl. Math. Lett. 93, 40--45 (2019; Zbl 1414.65026) Full Text: DOI
Wang, Junjie; Xiao, Aiguo; Wang, Chenxi A conservative difference scheme for space fractional Klein-Gordon-Schrödinger equations with a high-degree Yukawa interaction. (English) Zbl 1468.65114 East Asian J. Appl. Math. 8, No. 4, 715-745 (2018). MSC: 65M06 65N06 65M12 35Q55 35R11 PDFBibTeX XMLCite \textit{J. Wang} et al., East Asian J. Appl. Math. 8, No. 4, 715--745 (2018; Zbl 1468.65114) Full Text: DOI
Huang, Yunqing; Li, Xueyang; Xiao, Aiguo Fourier pseudospectral method on generalized sparse grids for the space-fractional Schrödinger equation. (English) Zbl 1419.65079 Comput. Math. Appl. 75, No. 12, 4241-4255 (2018). MSC: 65M70 35R11 35Q41 PDFBibTeX XMLCite \textit{Y. Huang} et al., Comput. Math. Appl. 75, No. 12, 4241--4255 (2018; Zbl 1419.65079) Full Text: DOI
Bu, Weiping; Xiao, Aiguo; Zeng, Wei Finite difference/finite element methods for distributed-order time fractional diffusion equations. (English) Zbl 1375.65110 J. Sci. Comput. 72, No. 1, 422-441 (2017). Reviewer: K. N. Shukla (Gurgaon) MSC: 65M06 65M60 35K05 35R11 65M20 65M12 PDFBibTeX XMLCite \textit{W. Bu} et al., J. Sci. Comput. 72, No. 1, 422--441 (2017; Zbl 1375.65110) Full Text: DOI
Shi, Long; Yu, Zuguo; Mao, Zhi; Xiao, Aiguo; Huang, Hailan Space-time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model. (English) Zbl 1395.35198 Physica A 392, No. 23, 5801-5807 (2013). MSC: 35R11 35R60 60G50 35B40 PDFBibTeX XMLCite \textit{L. Shi} et al., Physica A 392, No. 23, 5801--5807 (2013; Zbl 1395.35198) Full Text: DOI arXiv
Wang, Dongling; Xiao, Aiguo; Yang, Wei Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative. (English) Zbl 1297.65100 J. Comput. Phys. 242, 670-681 (2013). MSC: 65M06 65M12 35Q55 35R11 PDFBibTeX XMLCite \textit{D. Wang} et al., J. Comput. Phys. 242, 670--681 (2013; Zbl 1297.65100) Full Text: DOI
Wang, Dongling; Xiao, Aiguo Fractional variational integrators for fractional variational problems. (English) Zbl 1239.49028 Commun. Nonlinear Sci. Numer. Simul. 17, No. 2, 602-610 (2012). MSC: 49K15 34A08 49M30 PDFBibTeX XMLCite \textit{D. Wang} and \textit{A. Xiao}, Commun. Nonlinear Sci. Numer. Simul. 17, No. 2, 602--610 (2012; Zbl 1239.49028) Full Text: DOI
Yang, Shuiping; Xiao, Aiguo; Pan, Xinyuan Dependence analysis of the solutions on the parameters of fractional delay differential equations. (English) Zbl 1262.34009 Adv. Appl. Math. Mech. 3, No. 5, 586-597 (2011). MSC: 34A08 34A12 34K37 PDFBibTeX XMLCite \textit{S. Yang} et al., Adv. Appl. Math. Mech. 3, No. 5, 586--597 (2011; Zbl 1262.34009) Full Text: DOI
Ding, Zhiqing; Xiao, Aiguo; Li, Min Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients. (English) Zbl 1185.65146 J. Comput. Appl. Math. 233, No. 8, 1905-1914 (2010). Reviewer: Ivan Secrieru (Chişinău) MSC: 65M06 65M15 65M12 35R11 PDFBibTeX XMLCite \textit{Z. Ding} et al., J. Comput. Appl. Math. 233, No. 8, 1905--1914 (2010; Zbl 1185.65146) Full Text: DOI