Li, Xin; Liao, Hong-lin; Zhang, Luming A second-order fast compact scheme with unequal time-steps for subdiffusion problems. (English) Zbl 1466.65072 Numer. Algorithms 86, No. 3, 1011-1039 (2021). MSC: 65M06 65M15 65M12 65T50 35K57 35R11 PDFBibTeX XMLCite \textit{X. Li} et al., Numer. Algorithms 86, No. 3, 1011--1039 (2021; Zbl 1466.65072) Full Text: DOI
Ji, Bingquan; Liao, Hong-lin; Gong, Yuezheng; Zhang, Luming Adaptive second-order Crank-Nicolson time-stepping schemes for time-fractional molecular beam epitaxial growth models. (English) Zbl 1464.35229 SIAM J. Sci. Comput. 42, No. 3, B738-B760 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q35 65M06 65M12 76A20 35R11 PDFBibTeX XMLCite \textit{B. Ji} et al., SIAM J. Sci. Comput. 42, No. 3, B738--B760 (2020; Zbl 1464.35229) Full Text: DOI arXiv
Liao, Feng; Zhang, Luming; Wang, Tingchun Two energy-conserving and compact finite difference schemes for two-dimensional Schrödinger-Boussinesq equations. (English) Zbl 1456.65071 Numer. Algorithms 85, No. 4, 1335-1363 (2020). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{F. Liao} et al., Numer. Algorithms 85, No. 4, 1335--1363 (2020; Zbl 1456.65071) Full Text: DOI
Li, Xin; Zhang, Luming An efficient spectral-collocation difference method for two-dimensional Schrödinger equation with Neumann boundary conditions. (English) Zbl 1437.65214 Comput. Math. Appl. 79, No. 8, 2322-2335 (2020). MSC: 65N35 65M06 65T50 35Q55 35Q41 PDFBibTeX XMLCite \textit{X. Li} and \textit{L. Zhang}, Comput. Math. Appl. 79, No. 8, 2322--2335 (2020; Zbl 1437.65214) Full Text: DOI
Li, Xin; Zhang, Luming A conservative sine pseudo-spectral-difference method for multi-dimensional coupled Gross-Pitaevskii equations. (English) Zbl 1436.65106 Adv. Comput. Math. 46, No. 2, Paper No. 26, 30 p. (2020). MSC: 65M06 65N35 65M12 65M15 65T50 35Q55 PDFBibTeX XMLCite \textit{X. Li} and \textit{L. Zhang}, Adv. Comput. Math. 46, No. 2, Paper No. 26, 30 p. (2020; Zbl 1436.65106) Full Text: DOI
Li, Xin; Zhang, Luming; Liao, Hong-Lin Sharp \(H^1\)-norm error estimate of a cosine pseudo-spectral scheme for 2D reaction-subdiffusion equations. (English) Zbl 1440.65092 Numer. Algorithms 83, No. 3, 1223-1248 (2020). MSC: 65M06 65N35 65M12 65M15 26A33 35R11 35K57 PDFBibTeX XMLCite \textit{X. Li} et al., Numer. Algorithms 83, No. 3, 1223--1248 (2020; Zbl 1440.65092) Full Text: DOI
Liao, Feng; Zhang, Luming; Wang, Tingchun Unconditional \(L^{\infty}\) convergence of a conservative compact finite difference scheme for the N-coupled Schrödinger-Boussinesq equations. (English) Zbl 07041641 Appl. Numer. Math. 138, 54-77 (2019). MSC: 65-XX 65Txx 65Mxx 35Qxx PDFBibTeX XMLCite \textit{F. Liao} et al., Appl. Numer. Math. 138, 54--77 (2019; Zbl 07041641) Full Text: DOI
Liao, Feng; Zhang, Luming Optimal error estimates of explicit finite difference schemes for the coupled Gross-Pitaevskii equations. (English) Zbl 1499.65403 Int. J. Comput. Math. 95, No. 9, 1874-1892 (2018). MSC: 65M06 65N06 35Q55 35Q51 65M15 65M12 65L08 PDFBibTeX XMLCite \textit{F. Liao} and \textit{L. Zhang}, Int. J. Comput. Math. 95, No. 9, 1874--1892 (2018; Zbl 1499.65403) Full Text: DOI
Li, Xin; Zhang, Luming Error estimates of a trigonometric integrator sine pseudo-spectral method for the extended Fisher-Kolmogorov equation. (English) Zbl 1462.65163 Appl. Numer. Math. 131, 39-53 (2018). MSC: 65M70 65M06 65N35 65M15 35Q92 PDFBibTeX XMLCite \textit{X. Li} and \textit{L. Zhang}, Appl. Numer. Math. 131, 39--53 (2018; Zbl 1462.65163) Full Text: DOI
Zhou, Xuanxuan; Zhang, Luming A conservative compact difference scheme for the Zakharov equations in one space dimension. (English) Zbl 1387.65093 Int. J. Comput. Math. 95, No. 2, 279-302 (2018). MSC: 65M06 35Q53 PDFBibTeX XMLCite \textit{X. Zhou} and \textit{L. Zhang}, Int. J. Comput. Math. 95, No. 2, 279--302 (2018; Zbl 1387.65093) Full Text: DOI
Pan, Xintian; Zhang, Luming On the convergence of a high-accuracy conservative scheme for the Zakharov equations. (English) Zbl 1411.65115 Appl. Math. Comput. 297, 79-91 (2017). MSC: 65M06 65M70 35L70 35Q55 65M12 65M15 PDFBibTeX XMLCite \textit{X. Pan} and \textit{L. Zhang}, Appl. Math. Comput. 297, 79--91 (2017; Zbl 1411.65115) Full Text: DOI
Chen, Juan; Zhang, Lu-ming Numerical approximation of solution for the coupled nonlinear Schrödinger equations. (English) Zbl 1368.65132 Acta Math. Appl. Sin., Engl. Ser. 33, No. 2, 435-450 (2017). MSC: 65M06 65M30 35Q55 PDFBibTeX XMLCite \textit{J. Chen} and \textit{L.-m. Zhang}, Acta Math. Appl. Sin., Engl. Ser. 33, No. 2, 435--450 (2017; Zbl 1368.65132) Full Text: DOI
Liao, Feng; Zhang, Luming; Wang, Shanshan Numerical analysis of cubic orthogonal spline collocation methods for the coupled Schrödinger-Boussinesq equations. (English) Zbl 1368.65199 Appl. Numer. Math. 119, 194-212 (2017). MSC: 65M70 35Q55 35Q53 65M12 PDFBibTeX XMLCite \textit{F. Liao} et al., Appl. Numer. Math. 119, 194--212 (2017; Zbl 1368.65199) Full Text: DOI
Hu, Xiuling; Zhang, Luming An analysis of a second order difference scheme for the fractional subdiffusion system. (English) Zbl 1446.65067 Appl. Math. Modelling 40, No. 2, 1634-1649 (2016). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{X. Hu} and \textit{L. Zhang}, Appl. Math. Modelling 40, No. 2, 1634--1649 (2016; Zbl 1446.65067) Full Text: DOI
Liao, Feng; Zhang, Luming Conservative compact finite difference scheme for the coupled Schrödinger-Boussinesq equation. (English) Zbl 1360.65213 Numer. Methods Partial Differ. Equations 32, No. 6, 1667-1688 (2016). Reviewer: Charis Harley (Johannesburg) MSC: 65M06 35Q55 65M12 PDFBibTeX XMLCite \textit{F. Liao} and \textit{L. Zhang}, Numer. Methods Partial Differ. Equations 32, No. 6, 1667--1688 (2016; Zbl 1360.65213) Full Text: DOI
Hu, Xiuling; Zhang, Luming A new implicit compact difference scheme for the fourth-order fractional diffusion-wave system. (English) Zbl 1315.65073 Int. J. Comput. Math. 91, No. 10, 2215-2231 (2014). Reviewer: Vit Dolejsi (Praha) MSC: 65M06 65M12 35M30 35R11 65M15 PDFBibTeX XMLCite \textit{X. Hu} and \textit{L. Zhang}, Int. J. Comput. Math. 91, No. 10, 2215--2231 (2014; Zbl 1315.65073) Full Text: DOI
Hu, Xiuling; Zhang, Luming Conservative compact difference schemes for the coupled nonlinear Schrödinger system. (English) Zbl 1302.65192 Numer. Methods Partial Differ. Equations 30, No. 3, 749-772 (2014). Reviewer: Petr Sváček (Praha) MSC: 65M06 65M12 35Q55 PDFBibTeX XMLCite \textit{X. Hu} and \textit{L. Zhang}, Numer. Methods Partial Differ. Equations 30, No. 3, 749--772 (2014; Zbl 1302.65192) Full Text: DOI
Wang, Tingchun; Zhang, Luming; Jiang, Yong Convergence of an efficient and compact finite difference scheme for the Klein-Gordon-Zakharov equation. (English) Zbl 1329.65189 Appl. Math. Comput. 221, 433-443 (2013). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{T. Wang} et al., Appl. Math. Comput. 221, 433--443 (2013; Zbl 1329.65189) Full Text: DOI
Pan, Xintian; Zhang, Luming High-order linear compact conservative method for the nonlinear Schrödinger equation coupled with the nonlinear Klein-Gordon equation. (English) Zbl 1329.65185 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 92, 108-118 (2013). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{X. Pan} and \textit{L. Zhang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 92, 108--118 (2013; Zbl 1329.65185) Full Text: DOI
Sun, Qihang; Zhang, Luming; Wang, Shanshan; Hu, Xiuling A conservative compact difference scheme for the coupled Klein-Gordon-Schrödinger equation. (English) Zbl 1274.65240 Numer. Methods Partial Differ. Equations 29, No. 5, 1657-1674 (2013). MSC: 65M06 PDFBibTeX XMLCite \textit{Q. Sun} et al., Numer. Methods Partial Differ. Equations 29, No. 5, 1657--1674 (2013; Zbl 1274.65240) Full Text: DOI
Hu, Xiuling; Zhang, Luming Implicit compact difference schemes for the fractional cable equation. (English) Zbl 1252.74061 Appl. Math. Modelling 36, No. 9, 4027-4043 (2012). MSC: 74S20 65M06 35R11 74K10 PDFBibTeX XMLCite \textit{X. Hu} and \textit{L. Zhang}, Appl. Math. Modelling 36, No. 9, 4027--4043 (2012; Zbl 1252.74061) Full Text: DOI
Hu, Xiuling; Zhang, Luming On finite difference methods for fourth-order fractional diffusion-wave and subdiffusion systems. (English) Zbl 1262.65101 Appl. Math. Comput. 218, No. 9, 5019-5034 (2012). Reviewer: Muhammad Akram (Lahore) MSC: 65M06 35K51 35R11 65M12 PDFBibTeX XMLCite \textit{X. Hu} and \textit{L. Zhang}, Appl. Math. Comput. 218, No. 9, 5019--5034 (2012; Zbl 1262.65101) Full Text: DOI
Wang, Shanshan; Wang, Tingchun; Zhang, Luming; Guo, Boling Convergence of a nonlinear finite difference scheme for the Kuramoto-Tsuzuki equation. (English) Zbl 1221.65230 Commun. Nonlinear Sci. Numer. Simul. 16, No. 6, 2620-2627 (2011). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{S. Wang} et al., Commun. Nonlinear Sci. Numer. Simul. 16, No. 6, 2620--2627 (2011; Zbl 1221.65230) Full Text: DOI
Zhang, Luming; Bai, Dongmei; Wang, Shanshan Numerical analysis for a conservative difference scheme to solve the Schrödinger-Boussinesq equation. (English) Zbl 1230.65099 J. Comput. Appl. Math. 235, No. 17, 4899-4915 (2011). Reviewer: Petr Sváček (Praha) MSC: 65M06 65M12 65M15 35Q55 PDFBibTeX XMLCite \textit{L. Zhang} et al., J. Comput. Appl. Math. 235, No. 17, 4899--4915 (2011; Zbl 1230.65099) Full Text: DOI
Wang, Tingchun; Zhang, Luming; Chen, Fangqi Numerical analysis of a multi-symplectic scheme for a strongly coupled Schrödinger system. (English) Zbl 1158.65086 Appl. Math. Comput. 203, No. 1, 413-431 (2008). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65P10 37M15 37K05 35Q55 PDFBibTeX XMLCite \textit{T. Wang} et al., Appl. Math. Comput. 203, No. 1, 413--431 (2008; Zbl 1158.65086) Full Text: DOI