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
Tan, Tan; Bu, Wei-Ping; Xiao, Ai-Guo L1 method on nonuniform meshes for linear time-fractional diffusion equations with constant time delay. (English) Zbl 07568990 J. Sci. Comput. 92, No. 3, Paper No. 98, 26 p. (2022). MSC: 65-XX 35R11 65M06 65M60 65M12 PDFBibTeX XMLCite \textit{T. Tan} et al., J. Sci. Comput. 92, No. 3, Paper No. 98, 26 p. (2022; Zbl 07568990) Full Text: DOI
Li, Xue-Yang; Xiao, Ai-Guo Space-fractional diffusion equation with variable coefficients: well-posedness and Fourier pseudospectral approximation. (English) Zbl 1460.35376 J. Sci. Comput. 87, No. 1, Paper No. 28, 34 p. (2021). MSC: 35R11 35K20 65M12 65M70 65T40 PDFBibTeX XMLCite \textit{X.-Y. Li} and \textit{A.-G. Xiao}, J. Sci. Comput. 87, No. 1, Paper No. 28, 34 p. (2021; Zbl 1460.35376) 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
Wang, Junjie; Xiao, Aiguo Conservative Fourier spectral method and numerical investigation of space fractional Klein-Gordon-Schrödinger equations. (English) Zbl 1429.65254 Appl. Math. Comput. 350, 348-365 (2019). MSC: 65M70 35R11 35Q55 PDFBibTeX XMLCite \textit{J. Wang} and \textit{A. Xiao}, Appl. Math. Comput. 350, 348--365 (2019; Zbl 1429.65254) 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
Xiao, Aiguo; Wang, Chenxi; Wang, Junjie Conservative linearly-implicit difference scheme for a class of modified Zakharov systems with high-order space fractional quantum correction. (English) Zbl 1457.65065 Appl. Numer. Math. 146, 379-399 (2019). MSC: 65M06 35R11 35Q53 PDFBibTeX XMLCite \textit{A. Xiao} et al., Appl. Numer. Math. 146, 379--399 (2019; Zbl 1457.65065) 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
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
Wang, Dongling; Xiao, Aiguo; Yang, Wei Maximum-norm error analysis of a difference scheme for the space fractional CNLS. (English) Zbl 1339.65137 Appl. Math. Comput. 257, 241-251 (2015). MSC: 65M06 35R11 39B12 65M12 65M15 68W25 PDFBibTeX XMLCite \textit{D. Wang} et al., Appl. Math. Comput. 257, 241--251 (2015; Zbl 1339.65137) Full Text: DOI
Mao, Zhi; Xiao, Aiguo; Yu, Zuguo; Shi, Long Finite difference and sinc-collocation approximations to a class of fractional diffusion-wave equations. (English) Zbl 1442.65295 J. Appl. Math. 2014, Article ID 536030, 11 p. (2014). MSC: 65M70 35R11 65M06 65M12 PDFBibTeX XMLCite \textit{Z. Mao} et al., J. Appl. Math. 2014, Article ID 536030, 11 p. (2014; Zbl 1442.65295) Full Text: DOI
Wang, Dongling; Xiao, Aiguo; Yang, Wei A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations. (English) Zbl 1349.65339 J. Comput. Phys. 272, 644-655 (2014). MSC: 65M06 35R11 35Q55 PDFBibTeX XMLCite \textit{D. Wang} et al., J. Comput. Phys. 272, 644--655 (2014; Zbl 1349.65339) Full Text: DOI
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
Yang, Shuiping; Xiao, Aiguo; Su, Hong Convergence of the variational iteration method for solving multi-order fractional differential equations. (English) Zbl 1207.65109 Comput. Math. Appl. 60, No. 10, 2871-2879 (2010). MSC: 65L99 34A08 26A33 45J05 PDFBibTeX XMLCite \textit{S. Yang} et al., Comput. Math. Appl. 60, No. 10, 2871--2879 (2010; Zbl 1207.65109) 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