Xie, Jianqiang; Ali, Muhammad Aamir; Zhang, Zhiyue Time second-order splitting conservative difference scheme for nonlinear fractional Schrödinger equation. (English) Zbl 07781188 Math. Methods Appl. Sci. 46, No. 1, 1411-1422 (2023). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{J. Xie} et al., Math. Methods Appl. Sci. 46, No. 1, 1411--1422 (2023; Zbl 07781188) Full Text: DOI
Xie, Jianqiang; Wang, Quanxiang; Zhang, Zhiyue Conservative finite difference methods for the Boussinesq paradigm equation. (English) Zbl 07700839 Math. Comput. Simul. 206, 588-613 (2023). MSC: 65-XX 39-XX PDFBibTeX XMLCite \textit{J. Xie} et al., Math. Comput. Simul. 206, 588--613 (2023; Zbl 07700839) Full Text: DOI
Xie, Jianqiang; Yan, Xiao; Ali, Muhammad Aamir; Hammouch, Zakia A linear decoupled physical-property-preserving difference method for fractional-order generalized Zakharov system. (English) Zbl 07698134 J. Comput. Appl. Math. 426, Article ID 115044, 21 p. (2023). MSC: 65-XX 35L70 35R11 65M06 PDFBibTeX XMLCite \textit{J. Xie} et al., J. Comput. Appl. Math. 426, Article ID 115044, 21 p. (2023; Zbl 07698134) Full Text: DOI
Xie, Jianqiang; Zhang, Zhiyue Efficient high-order physical property-preserving difference methods for nonlinear fourth-order wave equation with damping. (English) Zbl 07691986 Comput. Math. Appl. 142, 64-83 (2023). MSC: 65M06 65M12 65M15 35Q35 65M60 PDFBibTeX XMLCite \textit{J. Xie} and \textit{Z. Zhang}, Comput. Math. Appl. 142, 64--83 (2023; Zbl 07691986) Full Text: DOI
Xie, Jianqiang; Liang, Dong; Zhang, Zhiyue Energy-preserving local mesh-refined splitting FDTD schemes for two dimensional Maxwell’s equations. (English) Zbl 07508494 J. Comput. Phys. 425, Article ID 109896, 29 p. (2021). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{J. Xie} et al., J. Comput. Phys. 425, Article ID 109896, 29 p. (2021; Zbl 07508494) Full Text: DOI
Xie, Jianqiang; Wang, Quanxiang; Zhang, Zhiyue Linear implicit finite difference methods with energy conservation property for space fractional Klein-Gordon-Zakharov system. (English) Zbl 1476.65196 Appl. Numer. Math. 167, 389-419 (2021). MSC: 65M06 65M12 82D10 76X05 26A33 35R11 PDFBibTeX XMLCite \textit{J. Xie} et al., Appl. Numer. Math. 167, 389--419 (2021; Zbl 1476.65196) Full Text: DOI
Xie, Jianqiang; Zhang, Zhiyue Efficient linear energy dissipative difference schemes for the coupled nonlinear damped space fractional wave equations. (English) Zbl 1450.35018 Commun. Nonlinear Sci. Numer. Simul. 90, Article ID 105291, 23 p. (2020). MSC: 35A35 35L82 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{J. Xie} and \textit{Z. Zhang}, Commun. Nonlinear Sci. Numer. Simul. 90, Article ID 105291, 23 p. (2020; Zbl 1450.35018) Full Text: DOI
Xie, Jianqiang; Liang, Dong; Zhang, Zhiyue Two novel energy dissipative difference schemes for the strongly coupled nonlinear space fractional wave equations with damping. (English) Zbl 1446.65080 Appl. Numer. Math. 157, 178-209 (2020). MSC: 65M06 65M12 35R11 26A33 PDFBibTeX XMLCite \textit{J. Xie} et al., Appl. Numer. Math. 157, 178--209 (2020; Zbl 1446.65080) Full Text: DOI
Xie, Jianqiang; Zhang, Zhiyue; Liang, Dong A new fourth-order energy dissipative difference method for high-dimensional nonlinear fractional generalized wave equations. (English) Zbl 1475.65085 Commun. Nonlinear Sci. Numer. Simul. 78, Article ID 104850, 21 p. (2019). MSC: 65M06 35L82 35R11 65M12 PDFBibTeX XMLCite \textit{J. Xie} et al., Commun. Nonlinear Sci. Numer. Simul. 78, Article ID 104850, 21 p. (2019; Zbl 1475.65085) Full Text: DOI
Xie, Jianqiang; Zhang, Zhiyue An analysis of implicit conservative difference solver for fractional Klein-Gordon-Zakharov system. (English) Zbl 1429.65202 Appl. Math. Comput. 348, 153-166 (2019). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{J. Xie} and \textit{Z. Zhang}, Appl. Math. Comput. 348, 153--166 (2019; Zbl 1429.65202) Full Text: DOI
Xie, Jianqiang; Zhang, Zhiyue An effective dissipation-preserving fourth-order difference solver for fractional-in-space nonlinear wave equations. (English) Zbl 1422.65192 J. Sci. Comput. 79, No. 3, 1753-1776 (2019). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{J. Xie} and \textit{Z. Zhang}, J. Sci. Comput. 79, No. 3, 1753--1776 (2019; Zbl 1422.65192) Full Text: DOI
Xie, Jianqiang; Zhang, Zhiyue; Liang, Dong A conservative splitting difference scheme for the fractional-in-space Boussinesq equation. (English) Zbl 1444.35132 Appl. Numer. Math. 143, 61-74 (2019). MSC: 35Q35 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{J. Xie} et al., Appl. Numer. Math. 143, 61--74 (2019; Zbl 1444.35132) Full Text: DOI
Xie, Jianqiang; Zhang, Zhiyue The high-order multistep ADI solver for two-dimensional nonlinear delayed reaction-diffusion equations with variable coefficients. (English) Zbl 1419.65036 Comput. Math. Appl. 75, No. 10, 3558-3570 (2018). MSC: 65M06 65M12 65M22 35K57 PDFBibTeX XMLCite \textit{J. Xie} and \textit{Z. Zhang}, Comput. Math. Appl. 75, No. 10, 3558--3570 (2018; Zbl 1419.65036) Full Text: DOI