Zhou, Bingzhen; Wang, Bo; Wang, Li-Lian; Xie, Ziqing A hybridizable discontinuous triangular spectral element method on unstructured meshes and its \(hp\)-error estimates. (English) Zbl 1517.65124 Numer. Algorithms 91, No. 3, 1231-1260 (2022). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N35 65N50 65D15 65N15 PDFBibTeX XMLCite \textit{B. Zhou} et al., Numer. Algorithms 91, No. 3, 1231--1260 (2022; Zbl 1517.65124) Full Text: DOI
Liu, Hongyan; Sheng, Changtao; Wang, Li-Lian; Yuan, Huifang On diagonal dominance of FEM stiffness matrix of fractional Laplacian and maximum principle preserving schemes for the fractional Allen-Cahn equation. (English) Zbl 1473.65207 J. Sci. Comput. 86, No. 2, Paper No. 19, 28 p. (2021). MSC: 65M60 65M06 65N30 35B50 41A05 41A25 41A58 15B05 26A33 35R11 PDFBibTeX XMLCite \textit{H. Liu} et al., J. Sci. Comput. 86, No. 2, Paper No. 19, 28 p. (2021; Zbl 1473.65207) Full Text: DOI arXiv
Sheng, Changtao; Shen, Jie; Tang, Tao; Wang, Li-Lian; Yuan, Huifang Fast Fourier-like mapped Chebyshev spectral-Galerkin methods for PDEs with integral fractional Laplacian in unbounded domains. (English) Zbl 1450.65154 SIAM J. Numer. Anal. 58, No. 5, 2435-2464 (2020). MSC: 65N35 65M70 41A05 41A25 35R11 26A33 35Q55 PDFBibTeX XMLCite \textit{C. Sheng} et al., SIAM J. Numer. Anal. 58, No. 5, 2435--2464 (2020; Zbl 1450.65154) Full Text: DOI arXiv
Tang, Tao; Wang, Li-Lian; Yuan, Huifang; Zhou, Tao Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains. (English) Zbl 1447.65161 SIAM J. Sci. Comput. 42, No. 2, A585-A611 (2020). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N35 65M70 41A05 41A25 35R11 26A33 65T50 PDFBibTeX XMLCite \textit{T. Tang} et al., SIAM J. Sci. Comput. 42, No. 2, A585--A611 (2020; Zbl 1447.65161) Full Text: DOI arXiv
Liu, Wenjie; Wang, Li-Lian Asymptotics of the generalized Gegenbauer functions of fractional degree. (English) Zbl 1435.30123 J. Approx. Theory 253, Article ID 105378, 25 p. (2020). MSC: 30E15 41A10 41A25 41A60 65G50 PDFBibTeX XMLCite \textit{W. Liu} and \textit{L.-L. Wang}, J. Approx. Theory 253, Article ID 105378, 25 p. (2020; Zbl 1435.30123) Full Text: DOI arXiv
Liu, Wenjie; Wang, Li-Lian; Xiang, Shuhuang A new spectral method using nonstandard singular basis functions for time-fractional differential equations. (English) Zbl 1463.65325 Commun. Appl. Math. Comput. 1, No. 2, 207-230 (2019). MSC: 65M70 35R11 65N35 65D05 PDFBibTeX XMLCite \textit{W. Liu} et al., Commun. Appl. Math. Comput. 1, No. 2, 207--230 (2019; Zbl 1463.65325) Full Text: DOI
Liu, Wenjie; Wang, Li-Lian; Li, Huiyuan Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces. (English) Zbl 1428.41020 Math. Comput. 88, No. 320, 2857-2895 (2019). Reviewer: Włodzimierz Łenski (Poznań) MSC: 41A25 41A10 41A50 65N35 65M60 PDFBibTeX XMLCite \textit{W. Liu} et al., Math. Comput. 88, No. 320, 2857--2895 (2019; Zbl 1428.41020) Full Text: DOI arXiv
Chen, Sheng; Shen, Jie; Wang, Li-Lian Laguerre functions and their applications to tempered fractional differential equations on infinite intervals. (English) Zbl 1398.65314 J. Sci. Comput. 74, No. 3, 1286-1313 (2018). MSC: 65N35 65E05 65M70 41A05 PDFBibTeX XMLCite \textit{S. Chen} et al., J. Sci. Comput. 74, No. 3, 1286--1313 (2018; Zbl 1398.65314) Full Text: DOI arXiv
Tang, Xiaojun; Shi, Yang; Wang, Li-Lian A new framework for solving fractional optimal control problems using fractional pseudospectral methods. (English) Zbl 1357.49157 Automatica 78, 333-340 (2017). MSC: 49R05 49J30 34A08 93C15 PDFBibTeX XMLCite \textit{X. Tang} et al., Automatica 78, 333--340 (2017; Zbl 1357.49157) Full Text: DOI
Yang, Zhiguo; Wang, Li-Lian; Rong, Zhijian; Wang, Bo; Zhang, Baile Seamless integration of global Dirichlet-to-Neumann boundary condition and spectral elements for transformation electromagnetics. (English) Zbl 1423.78008 Comput. Methods Appl. Mech. Eng. 301, 137-163 (2016). MSC: 78A25 78M22 PDFBibTeX XMLCite \textit{Z. Yang} et al., Comput. Methods Appl. Mech. Eng. 301, 137--163 (2016; Zbl 1423.78008) Full Text: DOI arXiv
Jiao, Yujian; Wang, Li-Lian; Huang, Can Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis. (English) Zbl 1349.65251 J. Comput. Phys. 305, 1-28 (2016). MSC: 65L60 34A08 41A05 PDFBibTeX XMLCite \textit{Y. Jiao} et al., J. Comput. Phys. 305, 1--28 (2016; Zbl 1349.65251) Full Text: DOI arXiv
Huang, Can; Jiao, Yujian; Wang, Li-Lian; Zhang, Zhimin Optimal fractional integration preconditioning and error analysis of fractional collocation method using nodal generalized Jacobi functions. (English) Zbl 1353.65086 SIAM J. Numer. Anal. 54, No. 6, 3357-3387 (2016). MSC: 65L70 34A08 65R20 45D05 45B05 65F08 65L60 65L05 PDFBibTeX XMLCite \textit{C. Huang} et al., SIAM J. Numer. Anal. 54, No. 6, 3357--3387 (2016; Zbl 1353.65086) Full Text: DOI
Chen, Sheng; Shen, Jie; Wang, Li-Lian Generalized Jacobi functions and their applications to fractional differential equations. (English) Zbl 1335.65066 Math. Comput. 85, No. 300, 1603-1638 (2016). MSC: 65L60 34A34 34B15 65L05 65L10 34A08 65L20 65L70 PDFBibTeX XMLCite \textit{S. Chen} et al., Math. Comput. 85, No. 300, 1603--1638 (2016; Zbl 1335.65066) Full Text: DOI arXiv
Samson, Michael Daniel; Li, Huiyuan; Wang, Li-Lian A new triangular spectral element method. I: Implementation and analysis on a triangle. (English) Zbl 1280.65131 Numer. Algorithms 64, No. 3, 519-547 (2013). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N30 65N35 65N22 65F05 35J05 PDFBibTeX XMLCite \textit{M. D. Samson} et al., Numer. Algorithms 64, No. 3, 519--547 (2013; Zbl 1280.65131) Full Text: DOI arXiv
Xie, Ziqing; Wang, Li-Lian; Zhao, Xiaodan On exponential convergence of Gegenbauer interpolation and spectral differentiation. (English) Zbl 1262.30023 Math. Comput. 82, No. 282, 1017-1036 (2013). MSC: 30E05 PDFBibTeX XMLCite \textit{Z. Xie} et al., Math. Comput. 82, No. 282, 1017--1036 (2013; Zbl 1262.30023) Full Text: DOI arXiv
Li, Youyun; Wang, Li-Lian; Li, Huiyuan; Ma, Heping A new spectral method on triangles. (English) Zbl 1216.65169 Hesthaven, Jan S. (ed.) et al., Spectral and high order methods for partial differential equations. Selected papers from the 8th ICOSAHOM ’09 conference, Trondheim, Norway, June 22–26, 2009. Berlin: Springer (ISBN 978-3-642-15336-5/hbk; 978-3-642-15337-2/ebook). Lecture Notes in Computational Science and Engineering 76, 237-246 (2011). MSC: 65N35 35J25 65N50 PDFBibTeX XMLCite \textit{Y. Li} et al., Lect. Notes Comput. Sci. Eng. 76, 237--246 (2011; Zbl 1216.65169) Full Text: DOI
Li, Huiyuan; Wang, Li-Lian A spectral method on tetrahedra using rational basis functions. (English) Zbl 1482.65218 Int. J. Numer. Anal. Model. 7, No. 2, 330-355 (2010). MSC: 65N35 35J05 41A20 65D12 PDFBibTeX XMLCite \textit{H. Li} and \textit{L.-L. Wang}, Int. J. Numer. Anal. Model. 7, No. 2, 330--355 (2010; Zbl 1482.65218) Full Text: Link
Wang, Zhong-Qing; Wang, Li-Lian A collocation method with exact imposition of mixed boundary conditions. (English) Zbl 1203.65052 J. Sci. Comput. 42, No. 2, 291-317 (2010). MSC: 65D30 65L60 65N35 PDFBibTeX XMLCite \textit{Z.-Q. Wang} and \textit{L.-L. Wang}, J. Sci. Comput. 42, No. 2, 291--317 (2010; Zbl 1203.65052) Full Text: DOI
Guo, Ben-yu; Wang, Li-Lian Error analysis of spectral method on a triangle. (English) Zbl 1116.65122 Adv. Comput. Math. 26, No. 4, 473-496 (2007). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N35 35J05 65N15 65N12 PDFBibTeX XMLCite \textit{B.-y. Guo} and \textit{L.-L. Wang}, Adv. Comput. Math. 26, No. 4, 473--496 (2007; Zbl 1116.65122) Full Text: DOI
Guo, Ben-yu; Wang, Li-lian Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces. (English) Zbl 1057.41003 J. Approximation Theory 128, No. 1, 1-41 (2004). Reviewer: Margit Lenard (Safat) MSC: 41A10 41A25 PDFBibTeX XMLCite \textit{B.-y. Guo} and \textit{L.-l. Wang}, J. Approx. Theory 128, No. 1, 1--41 (2004; Zbl 1057.41003) Full Text: DOI