Ge, Ang; Shen, Jinye; Vong, Seakweng Space-time methods based on isogeometric analysis for time-fractional Schrödinger equation. (English) Zbl 07784033 J. Sci. Comput. 97, No. 3, Paper No. 76, 33 p. (2023). MSC: 65M60 65D07 65M12 65M22 35Q55 35Q41 26A33 35R11 PDFBibTeX XMLCite \textit{A. Ge} et al., J. Sci. Comput. 97, No. 3, Paper No. 76, 33 p. (2023; Zbl 07784033) Full Text: DOI
Lyu, Pin; Vong, Seakweng A weighted ADI scheme with variable time steps for diffusion-wave equations. (English) Zbl 1526.65039 Calcolo 60, No. 4, Paper No. 49, 20 p. (2023). MSC: 65M06 65N06 65M12 35B65 26A33 35R11 PDFBibTeX XMLCite \textit{P. Lyu} and \textit{S. Vong}, Calcolo 60, No. 4, Paper No. 49, 20 p. (2023; Zbl 1526.65039) Full Text: DOI
Heydari, M. H.; Razzaghi, M. Highly accurate solutions for space-time fractional Schrödinger equations with non-smooth continuous solution using the hybrid clique functions. (English) Zbl 07695257 Math. Sci., Springer 17, No. 1, 31-42 (2023). MSC: 65-XX 45-XX PDFBibTeX XMLCite \textit{M. H. Heydari} and \textit{M. Razzaghi}, Math. Sci., Springer 17, No. 1, 31--42 (2023; Zbl 07695257) Full Text: DOI
Zhao, Guoye; An, Na; Huang, Chaobao Optimal error analysis of the Alikhanov formula for a time-fractional Schrödinger equation. (English) Zbl 1509.65104 J. Appl. Math. Comput. 69, No. 1, 159-170 (2023). MSC: 65M60 35R11 65M12 65M15 PDFBibTeX XMLCite \textit{G. Zhao} et al., J. Appl. Math. Comput. 69, No. 1, 159--170 (2023; Zbl 1509.65104) Full Text: DOI
Liu, Jianfeng; Wang, Tingchun; Zhang, Teng A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation. (English) Zbl 1506.65127 Numer. Algorithms 92, No. 2, 1153-1182 (2023). MSC: 65M06 65N06 65M12 65M15 35R11 35Q41 35Q55 PDFBibTeX XMLCite \textit{J. Liu} et al., Numer. Algorithms 92, No. 2, 1153--1182 (2023; Zbl 1506.65127) Full Text: DOI
Heydari, M. H.; Razzaghi, M.; Baleanu, D. A numerical method based on the piecewise Jacobi functions for distributed-order fractional Schrödinger equation. (English) Zbl 07609370 Commun. Nonlinear Sci. Numer. Simul. 116, Article ID 106873, 15 p. (2023). MSC: 65Mxx PDFBibTeX XMLCite \textit{M. H. Heydari} et al., Commun. Nonlinear Sci. Numer. Simul. 116, Article ID 106873, 15 p. (2023; Zbl 07609370) Full Text: DOI
Niu, Yuxuan; Liu, Yang; Li, Hong; Liu, Fawang Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media. (English) Zbl 07594640 Math. Comput. Simul. 203, 387-407 (2023). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{Y. Niu} et al., Math. Comput. Simul. 203, 387--407 (2023; Zbl 07594640) Full Text: DOI
Chen, Li; Lü, Shujuan Spectral approximation for nonlinear time fractional Schrödinger equation on graded meshes. (English) Zbl 1513.35517 Int. J. Comput. Math. 99, No. 12, 2524-2541 (2022). MSC: 35R11 65M12 65M70 PDFBibTeX XMLCite \textit{L. Chen} and \textit{S. Lü}, Int. J. Comput. Math. 99, No. 12, 2524--2541 (2022; Zbl 1513.35517) Full Text: DOI
Qin, Hongyu; Wu, Fengyan; Ding, Deng A linearized compact ADI numerical method for the two-dimensional nonlinear delayed Schrödinger equation. (English) Zbl 1510.65206 Appl. Math. Comput. 412, Article ID 126580, 14 p. (2022). MSC: 65M06 35Q55 65M12 PDFBibTeX XMLCite \textit{H. Qin} et al., Appl. Math. Comput. 412, Article ID 126580, 14 p. (2022; Zbl 1510.65206) Full Text: DOI
Hendy, Ahmed S.; Zaky, Mahmoud A. Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation. (English) Zbl 1517.35206 Nonlinear Dyn. 103, No. 3, 2493-2507 (2021). MSC: 35Q55 35R11 65N30 PDFBibTeX XMLCite \textit{A. S. Hendy} and \textit{M. A. Zaky}, Nonlinear Dyn. 103, No. 3, 2493--2507 (2021; Zbl 1517.35206) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi Fourth-order alternating direction implicit difference scheme to simulate the space-time Riesz tempered fractional diffusion equation. (English) Zbl 1480.65200 Int. J. Comput. Math. 98, No. 11, 2137-2155 (2021). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Int. J. Comput. Math. 98, No. 11, 2137--2155 (2021; Zbl 1480.65200) Full Text: DOI
Fan, Wenping; Jiang, Xiaoyun Error analysis of the unstructured mesh finite element method for the two-dimensional time-space fractional Schrödinger equation with a time-independent potential. (English) Zbl 07476638 Int. J. Comput. Math. 98, No. 8, 1663-1682 (2021). MSC: 65Mxx 26A33 65M06 65M12 65M15 65M60 PDFBibTeX XMLCite \textit{W. Fan} and \textit{X. Jiang}, Int. J. Comput. Math. 98, No. 8, 1663--1682 (2021; Zbl 07476638) Full Text: DOI
Hicdurmaz, Betul Finite difference schemes for time-fractional Schrödinger equations via fractional linear multistep method. (English) Zbl 1480.65209 Int. J. Comput. Math. 98, No. 8, 1561-1573 (2021). MSC: 65M06 35Q41 PDFBibTeX XMLCite \textit{B. Hicdurmaz}, Int. J. Comput. Math. 98, No. 8, 1561--1573 (2021; Zbl 1480.65209) Full Text: DOI
She, Mianfu; Li, Lili; Tang, Renxuan; Li, Dongfang A novel numerical scheme for a time fractional Black-Scholes equation. (English) Zbl 1479.91446 J. Appl. Math. Comput. 66, No. 1-2, 853-870 (2021). MSC: 91G60 65M60 65M70 91G20 PDFBibTeX XMLCite \textit{M. She} et al., J. Appl. Math. Comput. 66, No. 1--2, 853--870 (2021; Zbl 1479.91446) Full Text: DOI
Chai, Li; Liu, Yang; Li, Hong Fourth-order compact difference schemes for the two-dimensional nonlinear fractional mobile/immobile transport models. (English) Zbl 1524.65324 Comput. Math. Appl. 100, 1-10 (2021). MSC: 65M06 35R11 65M12 26A33 35Q49 65M15 35B65 65N06 PDFBibTeX XMLCite \textit{L. Chai} et al., Comput. Math. Appl. 100, 1--10 (2021; Zbl 1524.65324) Full Text: DOI
Wang, Ying; Wang, Gang; Bu, Linlin; Mei, Liquan Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation. (English) Zbl 1496.65174 Numer. Algorithms 88, No. 1, 419-451 (2021). MSC: 65M60 65N30 65M15 65M12 26A33 35R11 81Q05 35Q41 35Q55 PDFBibTeX XMLCite \textit{Y. Wang} et al., Numer. Algorithms 88, No. 1, 419--451 (2021; Zbl 1496.65174) Full Text: DOI
Wang, Zhibo; Liang, Yuxiang; Mo, Yan A novel high order compact ADI scheme for two dimensional fractional integro-differential equations. (English) Zbl 1476.65194 Appl. Numer. Math. 167, 257-272 (2021). MSC: 65M06 65N06 65M12 35R09 45J05 26A33 35R11 PDFBibTeX XMLCite \textit{Z. Wang} et al., Appl. Numer. Math. 167, 257--272 (2021; Zbl 1476.65194) Full Text: DOI
Li, Lili; She, Mianfu; Niu, Yuanling Fractional Crank-Nicolson-Galerkin finite element methods for nonlinear time fractional parabolic problems with time delay. (English) Zbl 1472.65123 J. Funct. Spaces 2021, Article ID 9981211, 10 p. (2021); corrigendum ibid. 2022, Article ID 9820258, 10 p. (2022). MSC: 65M60 65M06 65N30 65M15 35K55 35R07 35R11 PDFBibTeX XMLCite \textit{L. Li} et al., J. Funct. Spaces 2021, Article ID 9981211, 10 p. (2021; Zbl 1472.65123) Full Text: DOI arXiv
Abbaszadeh, Mostafa; Dehghan, Mehdi Numerical investigation of reproducing kernel particle Galerkin method for solving fractional modified distributed-order anomalous sub-diffusion equation with error estimation. (English) Zbl 1474.65340 Appl. Math. Comput. 392, Article ID 125718, 21 p. (2021). MSC: 65M60 34A34 26A33 35R11 65M12 65M75 65M15 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Math. Comput. 392, Article ID 125718, 21 p. (2021; Zbl 1474.65340) Full Text: DOI
Zhang, Chun-Hua; Jin, Jun-Wei; Sun, Hai-Wei; Sheng, Qin A spatially sixth-order hybrid \(L1\)-CCD method for solving time fractional Schrödinger equations. (English) Zbl 07332696 Appl. Math., Praha 66, No. 2, 213-232 (2021). Reviewer: Temur A. Jangveladze (Tbilisi) MSC: 65M06 65M20 65M60 PDFBibTeX XMLCite \textit{C.-H. Zhang} et al., Appl. Math., Praha 66, No. 2, 213--232 (2021; Zbl 07332696) Full Text: DOI
Eskar, Rena; Feng, Xinlong; Kasim, Ehmet On high-order compact schemes for the multidimensional time-fractional Schrödinger equation. (English) Zbl 1486.65101 Adv. Difference Equ. 2020, Paper No. 492, 17 p. (2020). MSC: 65M06 65M12 26A33 65M70 35R11 PDFBibTeX XMLCite \textit{R. Eskar} et al., Adv. Difference Equ. 2020, Paper No. 492, 17 p. (2020; Zbl 1486.65101) Full Text: DOI
Yan, Shaodan; Zhao, Fengqun; Li, Can; Zhao, Le High order WSGL difference operators combined with sinc-Galerkin method for time fractional Schrödinger equation. (English) Zbl 1492.65284 Int. J. Comput. Math. 97, No. 11, 2259-2286 (2020). MSC: 65M70 35R11 47B37 65M12 PDFBibTeX XMLCite \textit{S. Yan} et al., Int. J. Comput. Math. 97, No. 11, 2259--2286 (2020; Zbl 1492.65284) Full Text: DOI
Yang, Yin; Wang, Jindi; Zhang, Shangyou; Tohidi, Emran Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations. (English) Zbl 1488.65525 Appl. Math. Comput. 387, Article ID 124489, 17 p. (2020). MSC: 65M70 33C45 35Q40 41A55 41A25 65D32 35R09 45K05 45D05 35R11 26A33 65F10 PDFBibTeX XMLCite \textit{Y. Yang} et al., Appl. Math. Comput. 387, Article ID 124489, 17 p. (2020; Zbl 1488.65525) Full Text: DOI
Li, Dongfang; Zhang, Chengjian Long time numerical behaviors of fractional pantograph equations. (English) Zbl 1482.34189 Math. Comput. Simul. 172, 244-257 (2020). MSC: 34K37 65L03 65L05 65L07 65L12 65L20 PDFBibTeX XMLCite \textit{D. Li} and \textit{C. Zhang}, Math. Comput. Simul. 172, 244--257 (2020; Zbl 1482.34189) Full Text: DOI
Wang, Wenya; Cheng, Shuilin; Guo, Zhongkai; Yan, Xingjie A note on the continuity for Caputo fractional stochastic differential equations. (English) Zbl 1445.34027 Chaos 30, No. 7, 073106, 7 p. (2020). MSC: 34A08 34F05 34A12 PDFBibTeX XMLCite \textit{W. Wang} et al., Chaos 30, No. 7, 073106, 7 p. (2020; Zbl 1445.34027) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi A POD-based reduced-order Crank-Nicolson/fourth-order alternating direction implicit (ADI) finite difference scheme for solving the two-dimensional distributed-order Riesz space-fractional diffusion equation. (English) Zbl 1452.65145 Appl. Numer. Math. 158, 271-291 (2020). MSC: 65M06 65N06 65M99 65M15 65M12 65D30 35R11 26A33 35K57 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Numer. Math. 158, 271--291 (2020; Zbl 1452.65145) Full Text: DOI
Cheng, Xiujun; Qin, Hongyu; Zhang, Jiwei A compact ADI scheme for two-dimensional fractional sub-diffusion equation with Neumann boundary condition. (English) Zbl 1442.65152 Appl. Numer. Math. 156, 50-62 (2020). MSC: 65M06 65M12 26A33 35R11 PDFBibTeX XMLCite \textit{X. Cheng} et al., Appl. Numer. Math. 156, 50--62 (2020; Zbl 1442.65152) Full Text: DOI
Fei, Mingfa; Wang, Nan; Huang, Chengming; Ma, Xiaohua A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation. (English) Zbl 1436.65099 Appl. Numer. Math. 153, 399-411 (2020). MSC: 65M06 65M12 35Q41 35R11 26A33 PDFBibTeX XMLCite \textit{M. Fei} et al., Appl. Numer. Math. 153, 399--411 (2020; Zbl 1436.65099) Full Text: DOI
Li, Lili; Li, Dongfang Exact solutions and numerical study of time fractional Burgers’ equations. (English) Zbl 1427.35330 Appl. Math. Lett. 100, Article ID 106011, 7 p. (2020). MSC: 35R11 35Q53 65M60 65M70 PDFBibTeX XMLCite \textit{L. Li} and \textit{D. Li}, Appl. Math. Lett. 100, Article ID 106011, 7 p. (2020; Zbl 1427.35330) Full Text: DOI
Heydari, M. H.; Atangana, A. A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana-Baleanu-Caputo derivative. (English) Zbl 1483.65165 Chaos Solitons Fractals 128, 339-348 (2019). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{M. H. Heydari} and \textit{A. Atangana}, Chaos Solitons Fractals 128, 339--348 (2019; Zbl 1483.65165) Full Text: DOI
Li, Dongfang; Cao, Waixiang; Zhang, Chengjian; Zhang, Zhimin Optimal error estimates of a linearized Crank-Nicolson Galerkin FEM for the Kuramoto-Tsuzuki equations. (English) Zbl 1473.65310 Commun. Comput. Phys. 26, No. 3, 838-854 (2019). MSC: 65N30 65N12 65N15 35B45 PDFBibTeX XMLCite \textit{D. Li} et al., Commun. Comput. Phys. 26, No. 3, 838--854 (2019; Zbl 1473.65310) Full Text: DOI
Qin, Hongyu; Wu, Fengyan Several effective algorithms for nonlinear time fractional models. (English) Zbl 1433.65164 Appl. Math. Comput. 363, Article ID 124598, 13 p. (2019). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{H. Qin} and \textit{F. Wu}, Appl. Math. Comput. 363, Article ID 124598, 13 p. (2019; Zbl 1433.65164) Full Text: DOI
Zhang, Qifeng; Ren, Yunzhu; Lin, Xiaoman; Xu, Yinghong Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction-diffusion equations. (English) Zbl 1429.65207 Appl. Math. Comput. 358, 91-110 (2019). MSC: 65M06 35K57 35R11 65M12 PDFBibTeX XMLCite \textit{Q. Zhang} et al., Appl. Math. Comput. 358, 91--110 (2019; Zbl 1429.65207) Full Text: DOI
Chen, Xiaoli; Wu, Fengyan; Duan, Jinqiao; Kurths, Jürgen; Li, Xiaofan Most probable dynamics of a genetic regulatory network under stable Lévy noise. (English) Zbl 1428.92036 Appl. Math. Comput. 348, 425-436 (2019). MSC: 92C42 35Q84 PDFBibTeX XMLCite \textit{X. Chen} et al., Appl. Math. Comput. 348, 425--436 (2019; Zbl 1428.92036) Full Text: DOI arXiv
Cheng, Xiujun; Duan, Jinqiao; Li, Dongfang A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations. (English) Zbl 1429.65216 Appl. Math. Comput. 346, 452-464 (2019). MSC: 65M12 65M06 35R11 PDFBibTeX XMLCite \textit{X. Cheng} et al., Appl. Math. Comput. 346, 452--464 (2019; Zbl 1429.65216) Full Text: DOI
Fan, Wenping; Zhang, Hui The inverse problem and the second order \(\theta\) scheme with finite element method used for 2D nonlinear space fractional Schrödinger equation. (English) Zbl 1464.65101 Appl. Math. Lett. 98, 240-247 (2019). MSC: 65M32 65M60 65M06 65N30 65N50 62F15 35Q55 35R11 PDFBibTeX XMLCite \textit{W. Fan} and \textit{H. Zhang}, Appl. Math. Lett. 98, 240--247 (2019; Zbl 1464.65101) Full Text: DOI
Li, Dongfang; Wu, Chengda; Zhang, Zhimin Linearized Galerkin FEMs for nonlinear time fractional parabolic problems with non-smooth solutions in time direction. (English) Zbl 1418.65179 J. Sci. Comput. 80, No. 1, 403-419 (2019). MSC: 65N30 65N12 35K61 PDFBibTeX XMLCite \textit{D. Li} et al., J. Sci. Comput. 80, No. 1, 403--419 (2019; Zbl 1418.65179) Full Text: DOI