汤涛
2020-05-19
汤涛教授，数学研究中心主任，中国科学院院士、欧洲科学院院士
Email：ttang@uic.edu.cn
基本情况
汤教授1984年毕业于北京大学数学系，1989年获得英国利兹大学应用数学博士学位，其研究领域为计算数学，在高精度和自适应计算方法研究领域做出了重要学术成就，因此荣获冯康科学计算奖，教育部自然科学一等奖，国家自然科学二等奖。汤教授曾担任香港数学会理事长等重要学术职务。他还是数个著名学术刊物的主编、副主编或编委。
鉴于汤教授的学术影响力，他获选美国数学学会会士、美国工业与应用数学学会会士，并于2017年获选中国科学院院士，2018年获邀成为国际数学家大会报告人。
汤涛教授1990至1998年执教于加拿大西门菲莎大学，1998至2015年任职于香港浸会大学，历任数学系系主任、理学院院长、研究生院院长、协理副校长等多个重要职位。
汤教授是北师港浸大的创校校董，加入北师港浸大之前担任南方科技大学副校长兼教务长，数学系讲席教授。
研究领域
计算数学、数值分析、偏微分方程数值解
学习经历
英国利兹大学 数学 博士
北京大学 数学 学士
期刊出版物
1. Dong Li, Chaoyu Quan, and T. Tang Stability and convergence analysis for the implicit-explicit method to the Cahn-Hilliard equation, Mathematics of Computation, 91 (2022), pp. 785-809.
2. Dong Li, Chaoyu Quan, T. Tang and Wen Yang, On symmetry breaking of Allen-Cahn, accepted by CSIAM Transactions on Applied Mathematics (2022).
3. Hong-lin Liao, T. Tang, Tao Zhou, A new discrete energy technique for multi-step backward difference formulas, accepted by CSIAM Transactions on Applied Mathematics (2022).
4. T. Tang, Boyi Wang and Jiang Yang, Asymptotic analysis on the sharp interface limit of the time-fractional Cahn-Hilliard equation, accepted by SIAM J. Applied Math. (2022).
5. Hong-lin Liao, Tao Tang and Tao Zhou An energy stable and maximum bound preserving scheme with variable time steps for time fractional Allen-Cahn equation, SIAM J. Sci. Comput., 43(5) (2021), A3503–A3526.
6. Dong Li, Chaoyu Quan, and Tao Tang Stability and convergence analysis for the implicit-explicit method to the Cahn-Hilliard equation, accepted by Mathematics of Computation, (2021).
7. Dong Li and Tao Tang Stability of the semi-implicit method for the Cahn-Hilliard equation with logarithmic potentials, Ann. Appl. Math., 37 (2021), pp. 31-60.
8. Hong-lin Liao, Tao Tang and Tao Zhou An energy stable and maximum bound preserving scheme with variable time steps for time fractional Allen-Cahn equation, accepted by SIAM J. Sci. Cpmput. (2021).
9. Hong-lin Liao, Xuehua Song, Tao Tang and Tao Zhou Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection, Sci China Math, 64 (2021), pp. 887–902. https://doi.org/10.1007/s11425-020-1817-4
10. Hong-lin Liao, Tao Tang and Tao Zhou On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation, SIAM J. Numer. Anal. 58-4 (2020), pp. 2294-2314.
11. Hong-lin Liao, Tao Tang and Tao Zhou A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations. Accepted by J. Comput. Phys. (2020).
12. Chaoyu Quan, T. Tang and Jang Yang, How to Define Dissipation-Preserving Energy for Time-Fractional Phase-Field Equations. Accepted by CSIAM Transactions on Applied Mathematics (2020).
13. Changtao Sheng, Jie Shen, Tao Tang, Li-Lian Wang and Huifang Yuan Fast Fourier-like mapped Chebyshev Spectral-Galerkin methods for PDEs with integral fractional Laplacian in unbounded domains. Accepted by SIAM J. Numer. Anal. (2020).
14. Tao Tang Revisit of Semi-Implicit Schemes for Phase-Field Equations, Anal. Theory Appl., 36(3) (2020), 235-242.
15. Tao Tang and Zhonghua Qiao Efficient numerical methods for phase-field equations, Science Sinica Mathematica, 50(6) (2020), 1-20.
16. Tao Tang, Lilian Wang, Huifang Yuan, and Tao Zhou Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains , SIAM J. Sci. Comput., 42(2) (2020), A585-A611.
17. Zhiwei Fang, Jichun Li, Tao Tang and Tao Zhou, Efficient Stochastic Galerkin Methods for Maxwell's Equations with Random Inputs, J. Sci. Comput., 80(1) (2019), 248-267.
18. T. Tang, On effective numerical methods for phase-field models, Proceedings of the International Congress of Mathematicians, (ICM 2018), pp. 3669-3690 (2019). https://doi.org/10.1142/9789813272880_0196.
19. Tao Tang, Haijun Yu and Tao Zhou, On energy dissipation theory and numerical stability for time-fractional phase field equations, SIAM J. Sci. Comput. , 41(6) (2019), A3757-3778.
20. Guanghui Hu, Xucheng Meng and Tao Tang, On Robust and Adaptive Finite Volume Methods for Steady Euler Equations, in "Theory, Numerics and Applications of Hyperbolic Problems II", Springer, 2018, pp. 1-19.
21. T. Tang and J. Yang, Computing the maximal eigenpairs of large size tridiagonal matrices with O(1) number of iterations, Numer. Math. Theor. Meth. Appl. 11(4) (2018), 877-894.
22. T. Tang, H. Yuan and T. Zhou, Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains, 10.4208/cicp.2018.hh80.12 Commun. Comput. Phys., 24 (2018), 1143-1168.
23. B. Gong, W. Liu, T. Tang, W. Zhao, and T. Zhou, An efficient gradient projection method for Stochastic optimal control problems, SIAM J. Numer. Anal. 55(6) (2017), 2982-3005.
24. T. Hou, T. Tang and J. Yang, Numerical analysis of fully discretized Crank--Nicolson scheme for fractional-in-space Allen-Cahn equations, J. Sci. Comput., 72 (2017), 1214–1231.
25. X. Li, Z. Qiao and T. Tang, Gradient bounds for a thin film epitaxy equation, J. Diff. Eqns. 262 (2017), 1720-1746.
26. T. Tang, W. Zhao and T. Zhou Deferred correction methods for forward backward Stochastic differential equations, Numer. Math. Theor. Meth. Appl. 10(2) (2017), 222-242.
27. Z. Yang, T. Tang and J. Zhang Blowup of Volterra Integro-Differential Equations and Applications to Semi-Linear Volterra Diffusion Equations, Numer. Math. Theor. Meth. Appl. 10(4) (2017), 737-759.
28. H. Brunner, T. Tang and J. Zhang, Numerical blow-up of semilinear parabolic integro-differential equations on unbounded domain, J. Sci. Comput. 68 (2016), 1281-1298.
29. D. Li, Z. Qiao, and T. Tang, Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations, SIAM J. Numer. Anal. 54(3) (2016), 1653-1681.
30. X. Li, T. Tang and C. Xu, Numerical solutions for weakly singular volterra integral equations using Chebyshev and Legendre pseudo-spectral Galerkin methods, J. Sci. Comput. 67 (2016), 43–64.
31. F. Luo, T. Tang and H. Xie, Parameter-Free Time Adaptivity Based on Energy Evolution for the Cahn-Hilliard Equation, Commu. Comput. Phys. 19 (2016), 1542-1563.
32. J. Shen, T. Tang, and J. Yang, On The Maximum Principle Preserving Schemes For The Generalized Allen-Cahn Equation, Commu. Math. Sci. 14(6) (2016), 1517-1534.
33. T. Tang, and J. Yang, Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle, J. Comp. Math. 34 (2016), 471-481.
34. Y. Cheng, A. Kurganov, Z. Qu and T. Tang, Fast and stable explicit operator splitting methods for phase-field models, J. Comput. Phys. 303 (2015), 45-65.
35. V. D. Didenko, T. Tang and A. M. Vu, Spline Galerkin methods for the Sherman-Lauricella equation on contours with corners, SIAM J. Numer. Anal. 53(6) (2015), 2752-2770.
36. X. Feng, T. Tang and J. Yang, Long time numerical simulations for phase-field problems using p-adaptive spectral deferred correction methods, SIAM J. Sci. Comput. 37 (2015), A271-A294.
37. Z. Qiao, T. Tang and H. Xie Error analysis of a mixed finite element method for the molecular beam epitaxy model, SIAM J. Numer. Anal. 53 (2015), 184-205.
38. T. Tang and T. Zhou Recent developments in high order numerical methods for uncertainty quantification, (in Chinese), Sci. Sin. Math. 45 (2015), 891–928.
39. H. Dong, Z-H Quiao, S-Y Sun, and T. Tang, Adaptive moving grid methods for two-phase flow in porous media, J. Comput. Appl. Math. 265 (2014), 139-150.
40. T. Tang and T. Zhou, On discrete least square projection in unbounded domain with random evaluations and its application to parametric uncertainty quantification, SIAM J. Sci. Comput. 36(5) 2014, A2272-A2295.
41. Y. Chen, X. Li, and T. Tang, A note on Jacobi spectral-collocation methods for weakly singular volterra integral equations with smooth solutions, J. Comput. Math. 31 (2013), 47-56.
42. X. Feng, H. Song, T. Tang, and J. Yang, Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation, Inverse Problems and Imaging (A special issue in honor of Tony Chan's 60th birthday) 7 (2013), 679-695.
43. X. Feng, T. Tang, and J. Yang, Stabilized Crank-Nicolson/Adams-Bashforth schemes for phase field models, East Asian Journal on Applied Mathematics 3 (2013), no. 1, 59-80.
44. J. Huang, J. Lai, and T. Tang, An adaptive time stepping method with efficient error control for second-order evolution problems, Science China Mathematics 56 (2013), no. 12, 2735-2771.
45. X.-J. Li, T. Tang, and C.-J. Xu, Parallel in time algorithm with spectral-subdomain enhancement for volterra integral equations, SIAM J. Numer. Anal. 51 (2013), no. 3, 1735-1756.
46. T. Tang, H. Xie, and X. Yin, High-order convergence of spectral deferred correction methods on general quadrature nodes, J. Sci. Comput. 56 (2013), no. 1, 1-13.
47. G. Hu, Z. Qiao, and T. Tang, Moving finite element simulations for reaction-diffusion systems, Adv. Appl. Math. Mech. 4 (2012), no. 3, 365-381.
48. X.-J. Li and T. Tang, Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind, Front. Math. China 7 (2012), 69-84.
49. Z.-Q. Xie, X.-J. Li, and T. Tang, Convergence analysis of spectral Galerkin methods for Volterra type integral equations, J. Sci. Comput. 53 (2012), no. 2, 414-434.
50. Tao Zhou and Tao Tang, Galerkin methods for stochastic hyperbolic problems using bi-orthogonal polynomials, J. Sci. Comput. 51 (2012), 274-292.
51. Guanghui Hu, Ruo Li, and Tao Tang, A robust WENO type finite volume solver for steady Euler equations on unstructured grids, Commun. Comput. Phys. 9 (2011), 627-648.
52. Can Huang, Tao Tang, and Zhimin Zhang, Supergeometric convergence of spectral collocation methods for weakly singular Volterra and Fredholm integral equations with smooth solutions, J. Comput. Math. 29 (2011), 698-719.
53. Zhonghua Qiao, Zhengru Zhang, and Tao Tang, An adaptive time-stepping strategy for the molecular beam epitaxy models, SIAM J. Sci. Comput. 33 (2011), 1395-1414.
54. Fei Teng, Li Yuan, and Tao Tang, A speed-up strategy for finite volume WENO schemes for hyperbolic conservation laws, J. Sci. Comput. 46 (2011), 359-378.
55. Yubo Zhang and T. Tang, Simulating three-dimensional free surface viscoelastic flows using moving finite difference schemes, Numer. Math. Theor. Meth. Appl 4 (2011), 92-112.
56. Meiling Zhao, Zhonghua Qiao, and Tao Tang, A fast high order method for electromagnetic scattering by large open cavities, J. Comput. Math. 29 (2011), 287-304.
57. Yanping Chen and T. Tang, Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel, Math. Comp. 79 (2010), 147-167.
58. G.-H. Hu, R. Li, and T. Tang, A robust high-order residual distribution type scheme for steady Euler equations on unstructured grids, J. Comput. Phys. 229 (2010), 1681-1697.
59. T. Tang and Tao Zhou, Convergence analysis for stochastic collocation methods to scalar hyperbolic equations with a random wave speed, Commun. Comput. Phys. 8 (2010), 226-248.
60. Yubo Zhang, Heyu Wang, and Tao Tang, Simulating two-phase viscoelastic flows using moving finite element methods, Commun. Comput. Phys. 7 (2010), 333-349.
61. Tao Zhou and Tao Tang, Note on coefficient matrices from Stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 229 (2010), no. 22, 8225-8230.
62. Ishtiaq Ali, Hermann Brunner, and Tao Tang, A spectral method for pantograph-type delay differential equations and its convergence analysis, J. Comput. Math. 27 (2009), 254-265.
63. Ishtiaq Ali, H. Brunner, and T. Tang, Spectral methods for pantograph-type differential and integral equations with multiple delays, Front. Math. China 4 (2009), 49-61.
64. Yanping Chen and Tao Tang, Spectral methods for weakly singular Volterra integral equations with smooth solutions, J. Comput. Appl. Math. 233 (2009), 938-950.
65. T. Tang and Xiang Xu, Accuracy enhancement using spectral postprocessing for differential equations and integral equations, Commun. Comput. Phys. 5 (2009), 779-792.
66. Yinchuan Zhao, T. Tang, and Jinghua Wang, Regularity and global structure of solutions to Hamilton-Jacobi equations II. Convex initial data, J. Hyperbol. Differ. Eq. 6 (2009), no. 4, 709-723.
67. Y. Di, R. Li, and T. Tang, A general moving mesh framework in 3D and its application for simulating the mixture of multi-phase flows, Commun. Comput. Phys. 3 (2008), 582-603.
68. Jingtang Ma and T. Tang, Error analysis for a fast numerical method to a boundary integral equation of the first kind, J. Comput. Math. 26 (2008), 56-68.
69. T. Tang, Xiang Xu, and Jin Cheng, On spectral methods for Volterra type integral equations and the convergence analysis, J. Comput. Math. 26 (2008), 825-837.
70. H. Wang, R. Li, and T. Tang, Efficient computation of dentritic growth with r-adaptive finite element methods, J. Comput. Phys. 227 (2008), 5984-6000.
71. Y. Zhao, T. Tang, and J. Wang, Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonian, J. Hyperbol. Differ. Eq. 5 (2008), 663-680.
72. Y. Di, R. Li, T. Tang, and P. Zhang, Level set calculations for incompressible two-phase flows on a dynamically adaptive grid, J. Sci. Comput. 31 (2007), no. 1-2, 75-98.
73. Yinnian He, Yunxian Liu, and T. Tang, On large time-stepping methods for the Cahn-Hilliard equation, Appl. Numer. Math. 57 (2007), 616-628.
74. T. Tang and Z. H. Teng, Superconvergence of monotone difference schemes for piecewise smooth solutions of convex conservation laws, Hokkaido Math. J. 36 (2007), 849-874.
75. T. Tang, J. Wang, and Y. Zhao, On the piecewise smoothness of entropy solutions to scalar conservation laws for a large class of initial data, J. Hyperbol. Differ. Eq. 4 (2007), no. 3, 369-389.
76. L. Yuan and T. Tang, Resolving the shock-induced combustion by an adaptive mesh redistribution method, J. Comput. Phys. 224 (2007), 587-600.
77. Yana Di, Ruo Li, T. Tang, and Pingwen Zhang, Moving mesh methods for singular problems on a sphere using perturbed harmonic mappings, SIAM J. Sci. Comput. 28 (2006), 1490-1508.
78. R. Li and T. Tang, Moving mesh discontinuous Galerkin method for hyperbolic conservation laws, J. Sci. Comput. 27 (2006), 347-363.
79. Zhonghua Qiao, Zhilin Li, and T. Tang, A finite difference scheme for solving the nonlinear Poisson-Boltzmann equation modeling charged spheres, J. Comput. Math. 24 (2006), 252-264.
80. Z. Tang, T. Tang, and Z. Zhang, A simple moving mesh method for one- and two-dimensional phase-field equations, J. Comput. Appl. Math. 190 (2006), 252-269.
81. Chuanju Xu and T. Tang, Stability analysis of large time-stepping methods for epitaxial growth models, SIAM J. Numer. Anal. 44 (2006), 1759-1779.
82. Z. R. Zhang and T. Tang, Resolving small-scale structures in Boussinesq convection by adaptive grid methods, J. Comput. Appl. Math. 195 (2006), 274-291.
83. Boris N. Azarenok and T. Tang, Second-order Godunov-type scheme for reactive flow calculations on moving meshes, J. Comput. Phys. 206 (2005), 48-80.
84. Yana Di, Ruo Li, T. Tang, and Pingwen Zhang, Moving mesh finite element methods for the incompressible Navier-Stokes equations, SIAM J. Sci. Comput. 26 (2005), 1036-1056.
85. H. P. Ma, W. W. Sun, and T. Tang, Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains, SIAM J. Numer. Anal. 43 (2005), no. 1, 58-75.
86. Z. Yin, Li Yuan, and T. Tang, A new parallel strategy for two-dimensional incompressible flow simulations using pseudo-spectral methods, J. Comput. Phys. 210 (2005), 325-341.
87. Q. Y. Chen, T. Tang, and Z. H. Teng, A fast numerical method for integral equations of the first kind with logarithmic kernel using mesh grading, J. Comput. Math. 22 (2004), no. 2, 287-298.
88. Y. Q. Huang, Zhong-Ci Shi, T. Tang, and W. M. Xue, A multilevel successive iteration methods for nonlinear elliptic problems, Math. Comp. 73 (2004), no. 246, 525-539.
89. W.-B. Liu, H.-P. Ma, T. Tang, and N. Yan, A posteriori error estimates for DG time-stepping method for optimal control problems governed by parabolic equations, SIAM J. Numer. Anal. 42 (2004), no. 3, 1032-1061.
90. Z.-J. Tan, Z.-R. Zhang, Y.-Q. Huang, and T. Tang, Moving mesh methods with locally varying time steps, J. Comput. Phys. 200 (2004), 347-367.
91. H. Z. Tang, T. Tang, and K. Xu, A gas-kinetic scheme for shallow-water equations with source terms, Z. Angew. Math. Phys. 55 (2004), 365-382.
92. Boris N. Azarenok, Sergey A. Ivanenko, and T. Tang, Adaptive mesh redistribution method based on Godunov's scheme, Comm. Math. Sci. 1 (2003), no. 1, 152-179.
93. W. Sun, T. Tang, Michael J. Ward, and J. Wei, Numerical challenges for resolving spike dynamics for two one-dimensional reaction-diffusion systems, Stud. Appl. Math. 111 (2003), no. 1, 41-84.
94. H.-Z. Tang and T. Tang, Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal. 41 (2003), no. 2, 487-515.
95. H.-Z. Tang, T. Tang, and P.-W. Zhang, An adaptive mesh redistribution method for nonlinear Hamilton-Jacobi equations in two- and three dimensions, J. Comput. Phys. 188 (2003), no. 2, 543-572.
96. T. Tang, Z.-H. Teng, and Z.-P. Xin, Fractional rate of convergence for viscous approximation to nonconvex conservation laws, SIAM J. Math. Anal. 35 (2003), no. 1, 98-122.
97. Johnson C. M. Fok, B.-Y. Guo, and T. Tang, Combined Hermite spectral-finite difference method for the Fokker-Planck equations, Math. Comp. 71 (2002), 1497-1528.
98. R. Li, W.-B. Lin, H. P. Ma, and T. Tang, Adaptive finite element approximation for distributed elliptic optimal control problems, SIAM J. Control Optim. 41 (2002), 1321-1349.
99. R. Li, T. Tang, and P.-W. Zhang, A moving mesh finite element algorithm for singular problems in two and three space dimensions, J. Comput. Phys. 177 (2002), 365-393.
100. Z. Zhang and T. Tang, An adaptive mesh redistribution algorithm for convection-dominated problems, Comm. Pure Appl. Anal. 1 (2002), no. 3, 341-357.
101. Y. X. Kan, T. Tang, and Z.-H. Teng, On the piecewisely smooth solutions to non-homogeneous scalar conservation laws, J. Differential Equations 175 (2001), 27-50.
102. M. Li and T. Tang, A compact fourth-order finite difference scheme for unsteady viscous incompressible flows, J. Sci. Comput. 16 (2001), 29-46.
103. R. Li, T. Tang, and P.-W. Zhang, Moving mesh methods in multiple dimensions based on harmonic maps, J. Comput. Phys. 170 (2001), 562-588.
104. W.-B. Liu, H. P. Ma, and T. Tang, On mixed error estimates for elliptic obstacle problems, Adv. Comput. Math. 15 (2001), 261-283.
105. W.-B. Liu and T. Tang, Error analysis for a Galerkin-spectral method with coordinate transformation for solving singularly perturbed problems, Appl. Numer. Math. 38 (2001), 315-345.
106. H.-Z. Tang, T. Tang, and J.-H. Wang, On numerical entropy inequalities for second order relaxed scheme, Quart. of Appl. Math. 59 (2001), 391-399.
107. T. Tang, Z.-H. Teng, and J.-H. Wang, Convergence analysis of relazation schemes for conservation laws with stiff source terms, Methods and Applications of Analysis 8 (2001), 667-680.
108. T. Tang, W. M. Xue, and P. W. Zhang, Analysis of moving mesh methods based on geometrical variables, J. Comput. Math. 19 (2001), 41-54.
109. W. Z. Huang and T. Tang, Pseudospectral solutions for steady motion of a viscous fluid inside a circular boundary, Appl. Numer. Math. 33 (2000), 167-173.
110. S. McKee, T. Tang, and T. Diogo, An Euler-type method for two-dimensional Volterra integral equations of the first kind, IMA J. Numer. Anal. 20 (2000), 423-440.
111. Y. Qiu, D. M. Sloan, and T. Tang, Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: analysis of convergence, J. Comput. Appl. Math. 116 (2000), 121-143.
112. E. Tadmor and T. Tang, Pointwise error estimates for relaxation approximations to conservation laws, SIAM J. Math. Anal. 32 (2000), 870-886.
113. T. Tang and Z.-H. Teng, On the regularity of approximate solutions to conservation laws with piecewise smooth solutions, SIAM J. Numer. Anal. 38 (2000), 1483-1495.
114. T. Tang and J.-H. Wang, Convergence of MUSCL relaxing schemes to the relaxed schemes for conservation laws with stiff source terms, J. Sci. Comput. 15 (2000), 173-196.
115. E. Tadmor and T. Tang, Pointwise error estimates for scalar conservation laws with piecewise smooth solutions, SIAM J. Numer. Anal. 36 (1999), 1739-1758.
116. T. Tang and K. Xu, Gas-kinetic schemes for the compressible Euler equations: Positivity-preserving analysis, Z. Angew. Math. Phys. 50 (1999), 258-281.
117. T. Tang, Convergence analysis for operator splitting methods to conservation laws with stiff source terms, SIAM J. Numer. Anal. 35 (1998), 1939-1968.
118. T. Tang and Z. H. Teng, Viscosity methods for piecewise smooth solutions to scalar conservation laws, Math. Comp. 66 (1997), 495-526.
119. B. Jumarhon, W. Lamb, S. McKee, and T. Tang, A Volterra integral type method for solving a class of nonlinear initial-boundary value problems, Numerical Methods for Partial Differential Equations 12 (1996), 265-281.
120. A. Karageorghis and T. Tang, A spectral domain decomposition approach for steady Navier-Stokes problems in circular geometries, Comput. Fluids 25 (1996), 541-549.
121. M. Li and T. Tang, Steady viscous flow in a triangular cavity by efficient numerical techniques, Comput. Math. Appl. 31 (1996), 55-65.
122. M. Li, T. Tang, and B. Fornberg, A compact fourth order finite difference scheme for steady incompressible Navier-Stokes equations, Internat. J. Numer. Methods Fluids 20 (1995), 1137-1151.
123. Q. Sheng and T. Tang, Optimal convergence of an Euler and finite difference methodfor nonlinear partial integro-differential equations, Math. Comput. Modelling 21 (1995) no 10, 1-11.
124. T. Tang and Z. H. Teng, Error bounds for fractional step methods for conservation laws with source terms, SIAM J. Numer. Anal. 32 (1995), 110-127.
125. T. Tang and Z. H. Teng, The sharpness of Kuznetsov's O( sqrt Delta x) L1-error estimate for monotone difference schemes, Math. Comp. 64 (1995), 581-589.
126. T. Diogo, S. McKee, and T. Tang, Collocation methods for second-kind Volterra integral equations with weakly singular kernels, Proceedings of The Royal Society of Edinburgh, 124A, 1994, pp. 199-210.
127. B. Jumarhon, S. McKee, and T. Tang, The proof of an inequality arising in a reaction-diffusion study in a small cell, J. Comput. Appl. Math. 51 (1994), 99-101.
128. Y. Liu, L. Liu, and T. Tang, The numerical computation of connecting orbits in dynamical systems: a rational spectral approach, J. Comput. Phys. 111 (1994), 373-380.
129. Y. Song and T. Tang, On staggered Turkel-Zwas schemes for two dimensional shallow-water equations, Monthly Weather Review 122 (1994), 223-234.
130. E.-Z. Fu, T. Tang, and Z.-H. Teng, Riemann problem for a hyperbolic model of combustion: the Z-N-D solutions, J. Partial Differential Equations 6 (1993), 361-372.
131. Y. Song and T. Tang, Group velocity in numerical schemes for three dimensional hydrodynamic equations, J. Comput. Phys. 105 (1993), 72-82.
132. T. Tang, The Hermite spectral method for Gaussian type functions, SIAM J. Sci. Comput. 14 (1993), 594-606.
133. T. Tang, A finite difference scheme for partial integro-differential equations with weakly singular kernel, Appl. Numer. Math. 11 (1993), 309-319.
134. T. Tang, A note on collocation methods for Volterra integro-differential equations with weakly singular kernels, IMA J. Numer. Anal. 13 (1993), 93-99.
135. T. Diogo, S. McKee, and T. Tang, Product integration methods for an integral equation with logarithmic singular kernel, Appl. Numer. Math. 9 (1992), 259-266.
136. D. B. Ingham and T. Tang, Multi-grid solutions for steady state flow past a cascade of sudden expansions, Comput. Fluids 21 (1992), 647-660.
137. T. Tang, Superconvergence of numerical solutions to weakly singular Volterra integro-differential equations, Numer. Math. 61 (1992), 373-382.
138. T. Tang, S. McKee, and M. W. Reeks, A spectral method for the numerical solutions of a kinetic equation describing the dispersion of small particles in a turbulent flow, J. Comput. Phys. 103 (1992), 222-230.
139. T. Diogo, S. McKee, and T. Tang, A Hermite-type collocation method for the solution of an integral equation with a logarithmic singular kernel, IMA J. Numer. Anal. 11 (1991), 595-605.
140. D. B. Ingham, B. R. Morton, and T. Tang, Steady two-dimensional flow past a normal flat plat, Z. Angew. Math. Phys. 42 (1991), 584-604.
141. S. McKee, M. W. Reeks, and T. Tang, On a moving boundary solution to the Fokker-Planck equation for particle transport in turbulent flows with absorbing boundaries, IMA J. Appl. Math. 47 (1991), 307-318.
142. S. McKee and T. Tang, Integral inequalities and their application in numerical analysis, Fasc. Math. 23 (1991), 67-76.
143. T. Tang and D. B. Ingham, On steady flow past a rotating circular cylinder at Reynolds numbers 60 and 100, Comput. Fluids 19 (1991), 217-230.
144. D. B. Ingham and T. Tang, A numerical investigation into the steady flow past a rotating circular cylinder at low and intermediate Reynolds numbers, J. Comput. Phys. 87 (1990), 91-107.
145. D. B. Ingham, T. Tang, and B. R. Morton, Steady two dimensional flow through a row of normal flat plates, J. Fluid Mech. 210 (1990), 281-302.
146. T. Tang, On the collocation methods for high-order Volterra integro-differential equations, J. Comput. Math. (1990), 183-194.
147. T. Tang and W. Yuan, The numerical solution of second-order weakly singular Volterra integro-differential equations, J. Comput. Math. 8 (1990), 307-320.
148. W. Yuan and T. Tang, The numerical analysis of implicit Runge-Kutta methods for a certain nonlinear integro-differential equation, Math. Comp. 54 (1990), 155-168.
149. H. Brunner and T. Tang, Polynomial spline collocation methods for the nonlinear Basset equation, Comput. Math. Appl. 18 (1989), 449-457.
150. T. Tang, On three point second-order conservative finite difference schemes, J. Comput. Math. 5 (1987), 105-118.
151. T. Tang and W. Yuan, The further study of a certain integro-differential equation, J. Comput. Phys. 72 (1987), 486-497.
会议文献：
152. Li Yuan and T. Tang,
A comparison of high resolution schemes for hyperbolic chemically reacting flows,
Proceedings of the International Conference on Scientific Computing and Partial Differential Equations (Wenbin Liu, Michael Ng, and Zhong-Ci Shi, eds.), vol. 200, Science Press, Beijing, 2007, pp. 142-154.
153. T. Tang,
Moving mesh methods for computational fluid dynamics,
Recent Advances in Adaptive Computation (Z. Shi, Z. Chen, T. Tang, and D. Yu, eds.), Contemporary Mathematics, vol. 383, American Mathematical Society, 2005, Proceedings of the International Conference on Recent Advances in Adaptive Computation, May 2004, Hangzhou, China, pp. 141-173. (pdf)
154. H. P. Ma, W. W. Sun, and T. Tang,
Time-dependent hermite spectral methods for convection-diffusion equations in unbounded domains,
Advances in Scientific Computing and Applications (Beijing/New York) (Y. Lu, W. Sun, and T. Tang, eds.), Science Press, 2004, pp. 303-313.
155. H. Z. Tang and T. Tang,
Multi-dimensional moving mesh methods for shock computations,
Proceedings of the International Conference on Scientific Computing and Partial Differential Equations, 2002 (S. Y. Cheng, C. W. Shu, and T. Tang, eds.), American Mathematical Society, 2003, pp. 169-183. (pdf)
156. T. Tang and H. Z. Tang,
A moving mesh algorithm for one-dimensional nonlinear hyperbolic conservation laws,
Proceedings of The 5th China-Japan Seminar on Numerical Mathematics (in Shanghai, China, 2000) (Z.-C. Shi and Hideo Kawarada, eds.), Science Press, Beijing, NewYork, 2002, pp. 94-106.
157. T. Tang,
Error estimates for approximate solutions for nonlinear scalar conservation laws,
Proceedings of 8th International Conference on Hyperbolic Problems (in Magdeburg, Germany, 2000) (H. Freishler and G. Warnecke, eds.), International Series of Numerical Mathematics, vol. 141, 2001, pp. 873-882.
158. R. Li, W.-B. Liu, T. Tang, and P.-W. Zhang,
Moving mesh finite element methods based on harmonic maps,
Proceeding of Second International Workshop on Scientific Computing and Applications (Banff/Canada) (Banff/Canada, 2000) (P. Minev and Y. Lin, eds.), Advances in Computation: Theory and Practice, vol. 7, Nova Science Publishers, New York, 2001, pp. 143-156. (ps)
159. T. Tang and P.-W. Zhang,
Stability of moving mesh method for partial differential equations,
Proceedings of the Workshop on Scientific Computing'99 (Hong Kong, 1999) (Z.-C. Shi et al., ed.), Science Press, Beijing/New York, 2001, pp. 156-166.
160. E. Tadmor and T. Tang,
The optimal convergence rate of finite difference solutions for nonlinear conservation laws,
Proceedings of Seventh International Conference on Hyperbolic Problems (ETH Zurich, 1998) (M. Fey and R. Jelstch, eds.), International Series of Numerical Mathematics, vol. 130, 1999, pp. 925-934.
161. T. Tang and Z. H. Teng,
Monotone difference schemes for two dimensional nonhomogeneous conservation laws,
In Recent Advances in Differential Equations (Kunming, China) (H.-H. Dai and P. L. Sachdev, eds.), Longman, 1998, pp. 229-243.
162. D. Sloan and Tao Tang,
Adaptive numerical methods for singular perturbation problems,
Proceedings of the Workshop on Scientific Computing (Hong Kong) (G. Golub, S. H. Lui, F. Luk, and R. J. Plemmons, eds.), 1997, pp. 295-301.
163. W.-B. Liu and T. Tang,
Spectral methods for singular perturbation problems,
Proceedings of Symposia in Applied Mathematics (W. Gautschi, ed.), AMS, vol. 48, Amer. Math. Soc. (Providence), 1994, pp. 323-326.
164. T. Tang and Z. Teng,
Time-splitting methods for nonhomogeneous conservation laws,
Proceedings of Symposia in Applied Mathematics (W. Gautschi, ed.), AMS, vol. 48, Amer. Math. Soc. (Providence), 1994, pp. 389-393.
165. Y. Song and Tao Tang,
Dispersion relations of numerical schemes for the three-dimensional hydrodynamic equations,
Proceedings of the 7th International Conference on Numerical Methods in Laminar and Turbulent Flow (Swansea UK) (C. Taylor, J. H. Chin, and G. M. Homsy, eds.), Pineridge Press, 1991, pp. 1131-1141.
166. M. W. Reeks, K. Hyland, S. McKee, D. Swailes, and Tao Tang,
Analytic and numeric solutions for a Fokker-Planck type transport equation,
Symposium on Gas-Solid Flows, ASME, 1991, pp. 45-49.
167. D. B. Ingham and Tao Tang,
Steady flow past a cascade of sudden expansion,
Proceedings of the 6th International Conference on Numerical Methods for Laminar and Turbulent Flow, 1989, pp. 735-741.
168. E.-Z. Fu, T. Tang, and Z.-H. Teng,
Riemann problem for hyperbolic model of combustion: the existence and basic structure of the self-similar solutions,
Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, Contemporary Mathematics (W. B. Lindquist, ed.), vol. 100, 1989, pp. 335-354.
169. D. B. Ingham and T. Tang,
Numerical study of steady flow past a rotating circular cylinder,
Proceedings of the 11th International Conference on Numerical Methods for Fluid Dynamics, Lecture Notes in Physics, vol. 323, 1988, pp. 306-310.
出版书目
170. Numerical solution of differential equations: introduction to finite difference and finite element methods by Z Li, Z Qiao, T Tang, Cambridge University Press, 2017.
171. 《数学之英文写作》汤涛、丁玖，高等教育出版社，2013。
172. Spectral Methods: Algorithms, Analysis and Applications by Jie Shen, Tao Tang and L-L Wang, Springer, 2011.
173. Spectral and High-Order Methods with Applications by Jie Shen and Tao Tang, Science Press, 2007 (326 pp.).
编辑书目：
174. Adaptive Computations: Theory and Algorithms
Edited by Tao Tang and Jinchao Xu, Science Press, Beijing, 2007 (pp. 415)
175. Recent Advances in Adaptive Computation
Edited by Z.-C. Shi, Z. Chen, T. Tang and D. Yu, American Mathematical Society, 2005.
176. Advances in Scientific Computing and Applications
Edited by Yayan Lu, Weiwei Sun and Tao Tang, Science Press, Beijing/New York Publishers, 2004.
177. Recent Advances in Scientific Computing and Partial Differential Equations
Edited by S. Y. Cheng, C.-W. Shu and T. Tang, American Mathematical Society, 2003.
178. Recent Progress in Computational and Applied PDEs
Edited by Tony Chan, Yunqing Huang, Tao Tang, Jinchao Xu and Long-an Ying, Kluwer Academic/Plenum Publishers, 2002.
特别期刊：
179. Special Issue on Numerical analysis for functional differential and integral equations
Frontiers of Mathematics in China, Volume 4, Number 1 / March, 2009 Edited by Hermann Brunner, Tao Tang and Stefan Vandewalle
180. Special issue on Spectral and High Order Methods
Communications in Computational Physics, Volume 5, Issues 2-4 pp. 195-848, 2009
Edited by Zhiming Chen, Zhong-Ci Shi, Chi-Wang Shu and Tao Tang
181. Special Issue for the 2nd Sino-German Workshop on Computational and Applied Mathematics
Journal of Computational Mathematics, Vol.27, No.2-3, 2009
Edited by Carsten Carstensen, Rolf Rannacher, Zhong-Ci Shi and Tao Tang
182. Special Issue for the International Conference on Scientific Computing
Applied Numerical Mathematics, Volume 57, Issues 5-7, 2007Edited by Zhilin Li, Yongzhong Song and Tao Tang
183. Communications on Pure and Applied Analysis Volume 5, Number 2, June 2006 Edited by T. Diogo, P. Lima and T. Tang
184. Adaptive Computations Journal of Scientific Computing, Volume 24, Number 2, August 2005Edited by Tao Tang and Andy Wathen
其他著作
185. A new story on beautiful mind (in Chinese)
July, 2013
186. Zhang Yitang and Twin Prime Numbers (in Chinese)
July 19, 2013
187. Tang and Ding's book (in Chinese) (up to first section of Chapter 2)
February 5, 2012
188. Internationalization of Hong Kong's Higher Education (in Chinese)
Sing Tao, April 24, 2007. (Scanned newspaper article)
189. Postgraduate Studies at Hong Kong Baptist University
Ming Pao, January 20, 2006. (Scanned newspaper article)
190. 5th International Congress on Industrial and Applied Mathematics (in Chinese)
191. Collaboration of Postgraduate Programme
T. Tang. Ming Pao, A18 Jun. 2, 2003. (Scanned newspaper article)
192. Some Ideas on Hong Kong's Higher Education (in Chinese)
T. Tang. Ming Pao, D6, Nov. 2, 2001. (Scanned newspaper article) (ps)
