Qi, Ren-jun; Zhao, Xuan A unified design of energy stable schemes with variable steps for fractional gradient flows and nonlinear integro-differential equations. (English) Zbl 07801541 SIAM J. Sci. Comput. 46, No. 1, A130-A155 (2024). MSC: 35Q99 26A33 35R11 35R09 65M70 65M06 65N35 65N50 65M12 PDFBibTeX XMLCite \textit{R.-j. Qi} and \textit{X. Zhao}, SIAM J. Sci. Comput. 46, No. 1, A130--A155 (2024; Zbl 07801541) Full Text: DOI
Qi, Ren-jun; Zhang, Wei; Zhao, Xuan Variable-step numerical schemes and energy dissipation laws for time fractional Cahn-Hilliard model. (English) Zbl 07782670 Appl. Math. Lett. 149, Article ID 108929, 6 p. (2024). MSC: 65M06 65N06 65M70 65M12 26A33 35R11 PDFBibTeX XMLCite \textit{R.-j. Qi} et al., Appl. Math. Lett. 149, Article ID 108929, 6 p. (2024; Zbl 07782670) Full Text: DOI
Zhao, Xuan; Zhang, Haifeng; Sun, Hong Errors of an implicit variable-step BDF2 method for a molecular beam epitaxial model with slope selection. (English) Zbl 1527.65076 East Asian J. Appl. Math. 13, No. 4, 886-913 (2023). MSC: 65M06 35K57 65M12 PDFBibTeX XMLCite \textit{X. Zhao} et al., East Asian J. Appl. Math. 13, No. 4, 886--913 (2023; Zbl 1527.65076) Full Text: DOI arXiv
Sun, Hong; Chen, Yanping; Zhao, Xuan Error estimate of the nonuniform \(L1\) type formula for the time fractional diffusion-wave equation. (English) Zbl 1527.65074 Commun. Math. Sci. 21, No. 6, 1707-1725 (2023). MSC: 65M06 35R11 65M12 65M15 PDFBibTeX XMLCite \textit{H. Sun} et al., Commun. Math. Sci. 21, No. 6, 1707--1725 (2023; Zbl 1527.65074) Full Text: DOI arXiv
Xue, Zhongqin; Zhao, Xuan Compatible energy dissipation of the variable-step \(L1\) scheme for the space-time fractional Cahn-Hilliard equation. (English) Zbl 07749377 SIAM J. Sci. Comput. 45, No. 5, A2539-A2560 (2023). MSC: 65-XX 35R11 65M50 65M12 PDFBibTeX XMLCite \textit{Z. Xue} and \textit{X. Zhao}, SIAM J. Sci. Comput. 45, No. 5, A2539--A2560 (2023; Zbl 07749377) Full Text: DOI
Wei, Yiheng; Zhao, Xuan; Wei, Yingdong; Chen, Yangquan Lyapunov stability analysis for incommensurate nabla fractional order systems. (English) Zbl 1521.93149 J. Syst. Sci. Complex. 36, No. 2, 555-576 (2023). MSC: 93D20 93D30 93C20 35R11 PDFBibTeX XMLCite \textit{Y. Wei} et al., J. Syst. Sci. Complex. 36, No. 2, 555--576 (2023; Zbl 1521.93149) Full Text: DOI
Li, Juan; Sun, Hong; Zhao, Xuan Energy stable and convergent BDF3-5 schemes for the molecular beam epitaxial model with slope selection. (English) Zbl 1524.74042 Int. J. Comput. Math. 100, No. 7, 1646-1665 (2023). MSC: 74A50 35Q99 65M12 74K10 PDFBibTeX XMLCite \textit{J. Li} et al., Int. J. Comput. Math. 100, No. 7, 1646--1665 (2023; Zbl 1524.74042) Full Text: DOI
Zhao, Xuan; Liu, Zhengguang A symmetric mixed covolume method for the nonlinear parabolic problem. (English) Zbl 07532896 J. Appl. Math. Comput. 68, No. 3, 1591-1611 (2022). MSC: 65-XX 35K55 65M12 65M15 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{Z. Liu}, J. Appl. Math. Comput. 68, No. 3, 1591--1611 (2022; Zbl 07532896) Full Text: DOI
Sun, Hong; Zhao, Xuan; Cao, Haiyan; Yang, Ran; Zhang, Ming Stability and convergence analysis of adaptive BDF2 scheme for the Swift-Hohenberg equation. (English) Zbl 07526833 Commun. Nonlinear Sci. Numer. Simul. 111, Article ID 106412, 15 p. (2022). MSC: 65Mxx 35Kxx 35Bxx PDFBibTeX XMLCite \textit{H. Sun} et al., Commun. Nonlinear Sci. Numer. Simul. 111, Article ID 106412, 15 p. (2022; Zbl 07526833) Full Text: DOI
Zhao, Xuan; Li, Xiaoli; Li, Ziyan Fast and efficient finite difference method for the distributed-order diffusion equation based on the staggered grids. (English) Zbl 1486.65137 Appl. Numer. Math. 174, 34-45 (2022). MSC: 65M06 65M12 35R11 26A33 65M15 PDFBibTeX XMLCite \textit{X. Zhao} et al., Appl. Numer. Math. 174, 34--45 (2022; Zbl 1486.65137) Full Text: DOI
Liao, Hong-lin; Liu, Nan; Zhao, Xuan Asymptotically compatible energy of variable-step fractional BDF2 formula for time-fractional Cahn-Hilliard model. arXiv:2210.12514 Preprint, arXiv:2210.12514 [math.NA] (2022). MSC: 35Q99 65M06 65M12 74A50 BibTeX Cite \textit{H.-l. Liao} et al., ``Asymptotically compatible energy of variable-step fractional BDF2 formula for time-fractional Cahn-Hilliard model'', Preprint, arXiv:2210.12514 [math.NA] (2022) Full Text: arXiv OA License
Deng, Beichuan; Zhang, Zhimin; Zhao, Xuan Superconvergence points for the spectral interpolation of Riesz fractional derivatives. (English) Zbl 1434.65292 J. Sci. Comput. 81, No. 3, 1577-1601 (2019). MSC: 65N35 65N15 26A33 41A05 41A10 35R11 33C45 PDFBibTeX XMLCite \textit{B. Deng} et al., J. Sci. Comput. 81, No. 3, 1577--1601 (2019; Zbl 1434.65292) Full Text: DOI arXiv
Zhai, Shuying; Wang, Dongling; Weng, Zhifeng; Zhao, Xuan Error analysis and numerical simulations of Strang splitting method for space fractional nonlinear Schrödinger equation. (English) Zbl 1459.65204 J. Sci. Comput. 81, No. 2, 965-989 (2019). MSC: 65M70 65M12 65M15 35Q55 35R11 PDFBibTeX XMLCite \textit{S. Zhai} et al., J. Sci. Comput. 81, No. 2, 965--989 (2019; Zbl 1459.65204) Full Text: DOI
Sun, Hong; Zhao, Xuan; Sun, Zhi-Zhong The temporal second order difference schemes based on the interpolation approximation for the time multi-term fractional wave equation. (English) Zbl 1437.35696 J. Sci. Comput. 78, No. 1, 467-498 (2019). Reviewer: Ahmed M. A. El-Sayed (Alexandria) MSC: 35R11 65N06 35L05 35J05 45K05 60J60 60G50 60G51 42A38 PDFBibTeX XMLCite \textit{H. Sun} et al., J. Sci. Comput. 78, No. 1, 467--498 (2019; Zbl 1437.35696) Full Text: DOI
Zhao, Yue; Bu, Weiping; Zhao, Xuan; Tang, Yifa Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation. (English) Zbl 1380.65294 J. Comput. Phys. 350, 117-135 (2017). MSC: 65M60 65M12 35R11 35A15 PDFBibTeX XMLCite \textit{Y. Zhao} et al., J. Comput. Phys. 350, 117--135 (2017; Zbl 1380.65294) Full Text: DOI
Zhao, Xuan; Sun, Zhi-zhong; Karniadakis, George Em Second-order approximations for variable order fractional derivatives: algorithms and applications. (English) Zbl 1349.65092 J. Comput. Phys. 293, 184-200 (2015). MSC: 65D25 35R11 65M70 PDFBibTeX XMLCite \textit{X. Zhao} et al., J. Comput. Phys. 293, 184--200 (2015; Zbl 1349.65092) Full Text: DOI
Zhao, Xuan; Sun, Zhi-Zhong Compact Crank-Nicolson schemes for a class of fractional Cattaneo equation in inhomogeneous medium. (English) Zbl 1319.65084 J. Sci. Comput. 62, No. 3, 747-771 (2015). MSC: 65M06 35K20 65M12 35R11 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{Z.-Z. Sun}, J. Sci. Comput. 62, No. 3, 747--771 (2015; Zbl 1319.65084) Full Text: DOI
Zhao, Xuan; Xu, Qinwu Efficient numerical schemes for fractional sub-diffusion equation with the spatially variable coefficient. (English) Zbl 1429.65210 Appl. Math. Modelling 38, No. 15-16, 3848-3859 (2014). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{Q. Xu}, Appl. Math. Modelling 38, No. 15--16, 3848--3859 (2014; Zbl 1429.65210) Full Text: DOI
Zhao, Xuan; Sun, Zhi-Zhong; Hao, Zhao-Peng A fourth-order compact ADI scheme for two-dimensional nonlinear space fractional Schrödinger equation. (English) Zbl 1328.65187 SIAM J. Sci. Comput. 36, No. 6, A2865-A2886 (2014). MSC: 65M06 26A33 35R11 65M12 65M15 35Q55 PDFBibTeX XMLCite \textit{X. Zhao} et al., SIAM J. Sci. Comput. 36, No. 6, A2865--A2886 (2014; Zbl 1328.65187) Full Text: DOI
Ren, Jincheng; Sun, Zhi-Zhong; Zhao, Xuan Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions. (English) Zbl 1291.35428 J. Comput. Phys. 232, 456-467 (2013). MSC: 35R11 35N15 35K05 65M06 65M12 PDFBibTeX XMLCite \textit{J. Ren} et al., J. Comput. Phys. 232, 456--467 (2013; Zbl 1291.35428) Full Text: DOI
Zhang, Ya-Nan; Sun, Zhi-Zhong; Zhao, Xuan Compact alternating direction implicit scheme for the two-dimensional fractional diffusion-wave equation. (English) Zbl 1251.65126 SIAM J. Numer. Anal. 50, No. 3, 1535-1555 (2012). Reviewer: Kai Diethelm (Braunschweig) MSC: 65M06 65M12 65M15 35R11 35L05 PDFBibTeX XMLCite \textit{Y.-N. Zhang} et al., SIAM J. Numer. Anal. 50, No. 3, 1535--1555 (2012; Zbl 1251.65126) Full Text: DOI
Li, Juan; Sun, Zhizhong; Zhao, Xuan A three level linearized compact difference scheme for the Cahn-Hilliard equation. (English) Zbl 1262.65106 Sci. China, Math. 55, No. 4, 805-826 (2012). Reviewer: Muhammad Akram (Lahore) MSC: 65M06 65M12 65M15 35Q35 PDFBibTeX XMLCite \textit{J. Li} et al., Sci. China, Math. 55, No. 4, 805--826 (2012; Zbl 1262.65106) Full Text: DOI
Zhao, Xuan; Sun, Zhi-Zhong A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions. (English) Zbl 1227.65075 J. Comput. Phys. 230, No. 15, 6061-6074 (2011). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M06 65M15 65M12 35R11 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{Z.-Z. Sun}, J. Comput. Phys. 230, No. 15, 6061--6074 (2011; Zbl 1227.65075) Full Text: DOI