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LIST OF PUBLICATIONS:
[1] Y.F. Tang, The Symplecticity of Multi-Step Methods, Computers Math. Applic., 25(3), 83-90 (1993).
[2] Y.F. Tang, Non-conservativity of the Traditional Schemes for Liouville and Contact
Systems, Computers Math. Applic., 25(8), 89-94 (1993).
[3] Y.F. Tang, The Necessary Condition for a Runge-Kutta Scheme to
be Symplectic for Hamiltonian Systems, Computers
Math. Applic., 26(1), 13-20
(1993).
[4] Y.F. Tang, Geodesic Flows on Compact Surfaces---As an Application of Hamiltonian
Formalism, Computers Math. Applic., 26(1), 21-33 (1993).
[5] Y.F. Tang, Formal Energy of a Symplectic Scheme for Hamiltonian
Systems and its Applications (I), Computers
Math. Applic., 27(7), 31-39
(1994).
[6] Y.F. Tang & Y.H. Long, Formal
Energy of Symplectic Scheme for Hamiltonian Systems and its Applications (II), Computers Math. Applic., 27(12), 31-39 (1994).
[7] Y.F. Tang, L. Vázquez, F. Zhang & V.M. Pérez-García,
Symplectic Methods for the Nonlinear Schrödinger Equation, Computers Math. Applic., 32(5),
73-83 (1996).
[8] Y.F. Tang, V.M. Pérez-García & L. Vázquez, Symplectic
Methods for the Ablowitz-Ladik Model, Appl.
Math. Computa., 82, 17-38 (1997).
[9] V.V. Konotop, V.M. Pérez-García, Y.F. Tang & L. Vázquez,
Interaction of a Dark Soliton with a Localized Impurity, Phys. Letters A, 236(4),
314-318 (1997).
[10] Y.F. Tang, A Note on Construction of Higher-order Symplectic
Schemes from Lower-order One via Formal Energies, J. Computa. Math., 17(6),
561-568 (1999).
[11] Y.F. Tang, On Conjugate Symplecticity of Multi-Step Methods, J. Computa. Math., 18(4), 431-438 (2000).
[12] A.G. Xiao & Y.F. Tang, Regularity Properties of One-Leg
Methods for Delay Differential Equations, Computers
Math. Applic., 41(3/4), 363-372
(2001).
[13] Y.F. Tang, A Note on the Construction of Symplectic
Schemes for Splitable Hamiltonian H=H_1+H_2+H_3, J. Computa. Math., 20(1), 89-96 (2002).
[14] Y.F. Tang, Expansion of Step-Transition Operator of Multi-Step
Method and Its Applications (I), J. Computa.
Math., 20(2), 185-196 (2002).
[15] J.B. Chen, M.Z. Qin & Y.F. Tang, Symplectic and
Multi-Symplectic Methods for the Nonlinear Schrödinger Equation, Computers Math. Applic., 43(8/9), 1095-1106 (2002).
[16] Y.F. Tang, A.G. Xiao & J.B. Chen, Is the Formal Energy of the
Mid-Point Rule Convergent? Computers
Math. Applic., 43(8/9),
1171-1181 (2002).
[17] Y.F. Tang, Symplectic Computation of Hamiltonian Systems (I), J. Computa. Math., 20(3), 267-276 (2002).
[18] Y.F. Tang, Expansion of Step-Transition Operator of Multi-Step Method and
its Applications (II), J. Computa. Math., 20(5), 461-478 (2002).
[19] A.G. Xiao & Y.F. Tang, Symplectic Properties of Multistep Runge-Kutta
Methods, Computers
Math. Applic., 44(3/4), 1329-1338 (2002).
[20] A.G. Xiao & Y.F. Tang, Order Properties of Symplectic Runge-Kutta-Nyström
Methods, Computers Math.
Applic., 47(1), 569-582 (2004).
[21] J.Z. Liu, Y.F. Tang & Z.R. Yang, The spread of disease
with birth and death on networks, JSTAT, P08008 (2004).
[22] J.Z. Liu & Y.F. Tang, An exponential distribution network, Chinese Physics, 14(4), 643-645 (2005).
[23] Q.D. Feng & Y.F. Tang, Expansions of Step-transition Operators of
Multi-step Methods and Order Barriers for Dahlquist Pairs, J. Computa. Math., 24(1),
45-58 (2006).
[24] S.W. Zheng, Y.F. Tang & J.L. Fu, Non-Noether Symmetries
and Lutzky Conservative Quantities of Nonholonomic Nonconservative Dynamical
Systems, Chinese Physics, 15(2), 243-248 (2006).
[25] S. Jiménez & Y.F. Tang, Analysis
of the Numerical Methods for a Fractional Dirac Equation, Paper 19 in Proceedings of the Fifth International
Conference on Engineering Computational Technology,
pp. 1-10, edited by B.H.V. Topping, G. Montero and R. Montenegro, Civil-Comp Press,
Stirlingshire, Scotland, 2006.
[26] A.G. Xiao & Y.F. Tang, Equilibrium Attractive Properties of A Class of
Multistep Runge-Kutta Methods, Appl.
Math. Computa., 173(2), 1068-1081
(2006).
[27] H.J. Liu, Y.F. Tang & J.L. Fu, Algebraic Structure and Poisson's
Theory of Mechanico-Electrical Systems, Chinese
Physics, 15(8), 1653-1661
(2006).
[28] D.G. Dai & Y.F. Tang, A Note on Symplecticity of Step-Transition
Mappings for Multi-Step Methods, J.
Computa. Appli. Math., 196(2), 474-477
(2006).
[29] J.L. Fu, L.Q. Chen, S. Jiménez & Y.F. Tang, Non-Noether
Symmetries and Lutzky Conserved Quantities for Mechanico-Electrical Systems, Physics Letters A, 358(1), 5-10 (2006).
[30] J.L. Fu, G.D. Dai, S. Jim\'enez \& Y.F. Tang, Discrete
Variational Principle and First Integrals of Lagrange-Maxwell Mechanico-Electrical
Dynamical Systems, Chinese Physics, 16(3), 570-577 (2007).
[31] H.J. Liu, J.L. Fu & Y.F. Tang, A Series of Non-Noether
Conservative Quantities and Mei Symmetries of Nonconservative Systems, Chinese Physics, 16(3), 599-604 (2007).
[32] Y.F. Tang, J.W. Cao, X.T. Liu & Y.C. Sun, Symplectic
Methods for the Ablowitz-Ladik Discrete Nonlinear Schrödinger Equation, Journal
of Physics A: Mathematical and
Theoretical, 40(10), 2425-2437
(2007).
[33] Q.D. Feng, Y.D. Jiao & Y.F. Tang, Conjugate Symplecticity of 2nd-Order
Linear Multi-Step Methods, J. Computa.
Appli. Math., 203(1), 6-14
(2007).
[34] Y.D. Jiao, G.D. Dai, Q.D. Feng & Y.F. Tang, Non-existence
of Conjugate-Symplectic Multi-Step Methods of Odd Order, J. Computa. Math., 25(6),
690-696 (2007).
[35] J.L. Fu, S. Jiménez, Y.F. Tang & L. Vázquez, Construction
of Exact Invariants of Time-Dependent Linear Nonholonomic Dynamical Systems, Physics Letters A, 372(10), 1555-1561 (2008).
[36] J.L. Fu, B.Y. Chen, Y.F. Tang & H. Fu,
Symplectic-Energy-First Integrators of Discrete Mechanico-Electrical Dynamical Systems, Chinese Physics B, 17(11), 3942-3952 (2008).
[37] H. Guan, Y.D. Jiao, J. Liu & Y.F. Tang, Explicit Symplectic Methods
for the Nonlinear Schrödinger Equation, Commun.
Comput. Phys., 6(3), 639-654
(2009).
[38] J.L. Fu, N.M. Nie, J.F. Huang, S. Jiménez, Y.F. Tang, L. Vázquez &
W.J. Zhao, Noether Conserved Quantities and Lie Point Symmetries of Difference
Lagrange-Maxwell Equations and Lattices, Chinese
Physics B, 18(7), 2634-2641
(2009).
[39] Y.M. Zhao, G.D. Dai, Y.F. Tang & Q.H. Liu, Symplectic Discretization
for Spectral Element Solution of Maxwell's Equations, JPA: Math. Thero., 42(32),
325203 (2009).
[40] Y.F. Tang, Y. Chen, M. Li, K. Liao,
N.M. Nie & X.Y. Pan, Fractional Calculus in China: Fractional Numerical Analysis, Memoirs of the Royal Academy of
Mathematical, Physical and Natural Sciences of Madrid: Mathematical Sciences Series, 35(1), 37-74 (2009).
[41] N.M. Nie, Y.M. Zhao, S. Jiménez, M. Li,
Y.F. Tang & L. Vázquez, Solving Two-Point Boundary Value Problems of
Fractional Differential Equations with Riemann-Liouville Derivatives (in
English), J Syst. Simul., 22(1), 20-24 (2010).
[42] Y.M. Zhao, C.P. He & Y.F. Tang,
Parallel Mulitgrid Smoothing: JGS vs. PGS (in Chinese), J
Syst.
Simul., 22(1),
38-40 (2010).
[43] Y.Z. Song & Y.F. Tang, Hierarchical-control-based output
Synchronization of Coexisting Attractor Networks, Chinese Physics B, 19(2),
020506 (2010).
[44] H.J. Zhu, L.Y. Tang, S.H. Song, Y.F. Tang & D.S. Wang, Symplectic
Wavelet Collocation Method for Hamiltonian Wave Equations, JCP, 229(7), 2550-2572 (2010).
[45] N.M. Nie, Y.M. Zhao, M. Li, X.T. Liu,
S. Jiménez, Y.F. Tang & L. Vázquez, Solving Two-Point Boundary Value
Problems of Fractional Differential Equations by Spline Collocation Methods, International Journal of Modeling, Simulation,
and Scientific Computing, 1(1),
117-132
(2010).
[46] T.S. Aleroev, H.T. Aleroeva, N.M. Nie &
Y.F. Tang, Boundary Value Problems for Differential Equations of Fractional
Order, Mem. Differential Equations Math.
Phys., 49, 21-82 (2010).
[47] P.A. He, Y.P. Zhang, Y.H. Yao, Y.F. Tang & X.Y. Nan, The
Graphical Representation of Protein Sequences Based on the Physicochemical
Properties and its Applications, JCC, 31(11), 2136-2142 (2010).
[48] J. Ding & Y.F. Tang, Non-convexity of the Dimension Function for Sierpiński
Pedal Triangles, Fractals, 18(2), 191-195 (2010).
[49] Q.D. Feng, J.F. Huang, N.M. Nie, Z.J.
Shang & Y.F. Tang, Implementing Arbitrarily High-Order Symplectic Methods via
Krylov Deferred Correction Technique, International
Journal of Modeling, Simulation, and Scientific Computing, 1(2), 277-301 (2010).
[50] T.S. Aleroev, H.T. Aleroeva, J.F. Huang,
N.M. Nie, Y.F. Tang & S.Y. Zhang, Features of Inflow of a Liquid to a Chink
in the Cracked Deformable Layer, International
Journal of Modeling, Simulation, and Scientific Computing, 1(3), 333-347 (2010).
[51] H.J. Zhu, Y.M. Chen, S.H. Song &
Y.F. Tang, Symplectic and Multi-Symplectic Schemes for the Two-Dimensional
Nonlinear Schrödinger Equation (in Chinese), Mathematica Numerica Sinica, 32(3),
315-326 (2010).
[52] H.J. Zhu, S.H. Song & Y.F. Tang, Multi-Symplectic Wavelet Collocation
Method for the
Nonlinear Schrödinger and Camassa-Holm
Equations, Computer Physics
Communications, 182(3), 616-627
(2011).
[53] Y. Chen, Y.J. Sun & Y.F. Tang, Energy-Preserving Numerical Methods for
Landau-Lifshitz Equation, JPA: Math. Theor., 44(29), 295207 (2011).
[54] R. Scherer, S.L. Kalla, Y.F. Tang & J.F. Huang, The Grünwald-Letnikov
Method for Fractional Differential Equations, Computers Math. Applic., 62(3),
902-917 (2011).
[55]
R.L. Zhang, J.F. Huang, Y.F. Tang & L. Vázquez, Revertible and Symplectic Methods for the
Ablowitz-Ladik Discrete Nonlinear Schrödinger
Equation, in GCMS '11 Proceedings of the 2011 Grand Challenges on Modeling and
Simulation Conference, pp. 297-306, Society for
Modeling & Simulation International, Vista, CA, 2011.
[56] J.F. Huang, Y.F. Tang & L. Vázquez, Convergence Analysis of a
Block-by-Block Method for Fractional Differential Equations, Numerical Mathematics: Theory, Methods and
Applications, 5(2), 229-241
(2012).
[57] J.F. Huang, Y.F. Tang, W.J. Wang & J.Y. Yang, A Compact Difference
Scheme for Time Fractional Diffusion Equation with Neumann Boundary Conditions, Communications in Computer and Information
Science: AsiaSim 2012, 323,
273-284 (2012).
[58] W.P. Bu, A.G. Xiao & Y.F. Tang, Finite Difference Methods for Space
Fractional Advection-Diffusion Equations with Variable Coefficients, Communications in Computer and Information Science:
System Simulation and Scientific Computing, 327, 95-104 (2012).
[59] T. Aleroev, M. Kirane & Y.F. Tang, Boundary Value
Problems for Differential Equations of Fractional Order, Ukrainian Mathematical Bulletin, 10(2), 158-175 (2013); also in Journal
of Mathematical Sciences, 194(5),
499-512 (2013).
[60] J.F. Huang, Y.F. Tang, L. Vázquez & J.Y. Yang, Two
Finite Difference Schemes for Time Fractional Diffusion-Wave Equation, Numerical Algorithms, 64(4), 707-720 (2013).
[61] N. Liu, Y.F. Tang, X.Z. Zhu, L. Tobón & Q.H. Liu, Higher-order Mixed Spectral
Element Method for Maxwell Eigenvalue Problem, Proceedings of 2013 IEEE Antennas and Propagation Society International
Symposium, AP-S 2013, pp. 1646-1647.
[62] N.M. Nie, J.F. Huang, W.J.
Wang & Y.F. Tang, Solving Spatial-Fractional Partial Differential Diffusion
Equations by Spectral Method, Journal of
Statistical Computation and Simulation, 84(6), 1173-1189 (2014).
[63] R.L. Zhang, J. Liu, Y.F. Tang, H. Qin, J.Y. Xiao
& B.B. Zhu, Canonicalization and Symplectic Simulation of the Gyrocenter
Dynamics in Time-Independent Magnetic Fields, Physics of Plasmas, 21(3), 032504 (2014).
[64] J.F. Huang, N.M. Nie & Y.F. Tang, A second Order
Finite Difference-Spectral Method for Space Fractional Diffusion Equations, SCIENCE CHINA Mathematics, 57(6), 1303-1317 (2014).
[65] J.Y. Yang, J.F. Huang, D.M. Liang & Y.F. Tang,
Numerical Solution of Fractional Diffusion-Wave Equation Based on Fractional
Multistep Method, Appl. Math. Modell., 38, 3652-3661 (2014).
[66] W.P. Bu, Y.F. Tang & J.Y. Yang,
Galerkin Finite Element Method for Two-Dimensional Riesz Space Fractional
Diffusion Equations, Journal of
Computational Physics, 276,
26-38 (2014).
[67] W. Jiang, N. Liu, Y.F. Tang & Q.H. Liu, Mixed
Finite Element Method for 2D Vector Maxwell's Eigenvalue Problem in an Anisotropic
Medium, Progress in Electromagnetic
Research, 148, 159-170 (2014).
[68] J.Y. Yang, Y.M. Zhao, N. Liu, W.P. Bu, T.L Xu &
Y.F. Tang, An Implicit MLS Meshless Method for 2-D Time Dependent Fractional
Diffusion-Wave Equation, Applied
Mathematical Modelling, 39(3-4),
1229-1240 (2015).
[69] N. Liu, L. Tobón, Y.F. Tang & Q.H. Liu, Mixed
Spectral Element Method for 2D Maxwell's Eigenvalue Problem, Commun. Comput. Phys., 17(2),458-486, (2015).
[70] W.P. Bu, X.T. Liu,
Y.F. Tang & J.Y. Yang, Finite Element Multigrid Method for Multi-Term Time
Fractional Advection Diffusion Equations, International
Journal of Modeling, Simulation, and Scientific Computing (IJMSSC), 6(1), 1540001, (2015).
[71] N. Liu, L. Tobón, Y.M. Zhao, Y.F. Tang & Q.H.
Liu, Mixed Spectral Element Method for 3D Maxwell's Eigenvalue Problem, IEEE: Transactions on Microwave Theory and
Techniques, 63(2), 317-325 (2015).
[72] W.P. Bu, Y.F. Tang, Y.C. Wu & J.Y. Yang,
Crank-Nicolson ADI Galerkin Finite Element Method for Two-Dimensional Fractional
FitzHugh-Nagumo Monodomain Model, Applied
Mathematics and Computation, 257,
355-364 (2015).
[73] Y.M. Zhao, W.P. Bu, J.F. Huang, D.Y. Liu & Y.F.
Tang, Finite Element Method for Two-Dimensional Space-Fractional
Advection-Dispersion Equations, Applied
Mathematics and Computation, 257,
553-565 (2015).
[74] W.P. Bu, Y.F. Tang, Y.C. Wu & J.Y.
Yang, Finite Difference/Finite Element Method for Two-Dimensional Space and
Time Fractional Bloch-Torrey Equations, Journal
of Computational Physics, 293, 264-279 (2015).
[75] M. Aleroev, T. Aleroev, M. Kirane & Y.F. Tang, On One Class of Persymmetric Matrices Generated by Boundary Value Problems for Differential Equations of Fractional Order, Applied Mathematics and Computation, 268, 151-164 (2015), http://dx.doi.org/10.1016/j.amc.2015.06.076.
[76]
N. Liu, G.X. Cai, C.H. Zhu, Y.F. Tang & Q.H. Liu, The Mixed Spectral
Element Method for Anisotropic, Lossy, and Open Waveguides, IEEE: Transactions on Microwave Theory and
Techniques, 63(10), 3094-3102,
(2015), http://dx.doi.org/10.1109/TMTT.2015.2472416.
[77] R.L. Zhang, Y.F.
Tang, B.B. Zhu, X.B. Tu & Y. Zhao, Convergence Analysis of the Formal
Energies of Symplectic Methods for Hamiltonian Systems, Science China Mathematics, 59(2): 379-396 (2016), http://dx.doi.org/10.1007/s11425-015-5003-7.
[78] B.B. Zhu, Z.X. Hu,
Y.F. Tang & R.L. Zhang, Symmetric and Symplectic Methods for Gyrocenter
Dynamics in Time-Independent Magnetic Fields, International Journal of Modeling, Simulation, and Scientific Computing
(IJMSSC), 7(3), 1650008, (2016), http://dx.doi.org/10.1142/S1793962316500082.
[79] R.L. Zhang, J.
Liu, H. Qin, Y.F. Tang, Y. He & Y.L. Wang, Application of Lie Algebra in
Constructing Volume-Preserving Algorithms for Charged Particles Dynamics, Commun. Comput. Phys., 19(5), 1397-1408 (2016),
http://dx.doi.org/ 10.4208/cicp.scpde14.33s.
[80] B.B. Zhu, R.L.
Zhang, Y.F. Tang, X.B. Tu & Y. Zhao, K-symplectic and symplectic methods
for non-canonical Hamiltonian systems, Journal
of Computational Physics, 322,
387-399 (2016), http://dx.doi.org/10.1016/j.jcp.2016.06.044.
[81] S. Arshad, D.
Baleanu, J.F. Huang, Y.F. Tang & M.M. Al-Qurashi, Dynamical Analysis of
Fractional Order Model of Immunogenic Tumors, Advances in Mechanical Engineering, 8(7), 1-13 (2016), http://dx.doi.org/10.1177/1687814016656704.
[82] R.L. Zhang, H.
Qin, Y.F. Tang, J. Liu, Yang He & J.Y. Xiao, Explicit Symplectic Algorithms
Based on Generating Functions for Charged Particle Dynamics, Physical Review E, 94(1), 013205 (2016), http://dx.doi.org/10.1103/PhysRevE.94.013205.
[83] X.B. Tu, B.B. Zhu,
Y.F. Tang, H. Qin, J. Liu & R.L. Zhang, A Family of New Explicit,
Revertible, Volume-Preserving Numerical Schemes for the Systems of Lorentz
Force, Physics of Plasmas, 23(12), 122514 (2016),
http://dx.doi.org/10.1063/1.4972878.
[84] Y.M. Zhao, P.
Chen, W.P. Bu, X.T. Liu & Y.F. Tang, Two Mixed Finite Element Methods for
Time-Fractional Diffusion Equations, Journal
of Scientific Computing, 70(1),
407-428 (2017), http://dx.doi.org/10.1007/s10915-015-0152-y.
[85] T.S. Aleroev, H.T.
Aleroeva, J.F. Huang, M.V. Tamm, Y.F. Tang & Y. Zhao, Boundary Value
Problems of Fractional Fokker-Plank Equations, Computers and Mathematics with Applications, 73(6), 959-969 (2017),
http://dx.doi.org/10.1016/j.camwa.2016.06.038.
[86] Y.M. Zhao, Y.D.
Zhang, F. Liu, I. Turner, Y.F. Tang & V. Anh, Convergence and
Superconvergence of a Fully-Discrete Scheme for Multi-Term Time Fractional
Diffusion Equations, Computers and
Mathematics with Applications, 73(6),
1087-1099 (2017), http://dx.doi.org/10.1016/j.camwa.2016.05.005.
[87] S. Arshad, D.
Baleanu, W.P. Bu & Y.F. Tang, Effects of HIV Infection on CD$4^+$ T Cell
Population Based on a Fractional Order Model, Advances in Difference Equations, 2017:92 (2017),
http://dx.doi.org/10.1186/s13662-017-1143-0.
[88] S. Arshad, J.F.
Huang, A.Q.M. Khaliq & Y.F. Tang, A second order finite difference method
for time-space fractional diffusion equations with Riesz derivative, Journal of Computational Physics, 350, 1-15 (2017),
http://dx.doi.org/10.1016/j.jcp.2017.08.038.
[89] Y. Zhao, W.P. Bu,
X. Zhao & Y.F. Tang, Galerkin finite element method for two-dimensional
space and time fractional Bloch-Torrey equations, Journal of Computational Physics, 350, 117-135 (2017), http://dx.doi.org/10.1016/j.jcp.2017.08.051.
[90] Z.G. Shi, Y.M.
Zhao, F. Liu, Y.F. Tang, F.L. Wang & Y.H. Shi, High accuracy analysis of an
$H^1$-Galerkin mixed finite element method for two-dimensional time fractional
diffusion equations, Computers and
Mathematics with Applications, 74,
1903-1914 (2017),
http://dx.doi.org/10.1016/j.camwa.2017.06.057.
[91] Q. Sheng, Y.F. Tang, B.A. Wade & Y.S. Wang, Recent trends in highly accurate and structure-preserving numerical methods for partial differential equations, International Journal of Computer Mathematics, 95(1), 1-2 (2018), http://dx.doi.org/10.1080/00207160.2017.1359884.
[92] S. Arshad, W.P. Bu, J.F. Huang, Y.F. Tang & Y. Zhao, Finite difference method for time-space linear and nonlinear fractional diffusion equations, International Journal of Computer Mathematics, 95(1), 202-217 (2018), http://dx.doi.org/10.1080/00207160.2017.1344231.
[93] Y.D. Zhang, Y.M. Zhao, F.L. Wang & Y.F. Tang, High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes, International Journal of Computer Mathematics, 95(1), 218-230 (2018), http://dx.doi.org/10.1080/00207160.2017.1401708.
[94] R.L. Zhang, Y.L. Wang, Y. He, J.Y. Xiao, J. Liu, H. Qin & Y.F. Tang, Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field, Physics of Plasmas, 25(2), 022117 (2018), https://doi.org/10.1063/1.5012767.
[95] Z.G. Shi, Y.M. Zhao, Y.F. Tang, F.L. Wang & Y.H. Shi, Superconvergence analysis of an $H^1$-Galerkin mixed finite element method for two-dimensional multi-term time fractional diffusion equations, International Journal of Computer Mathematics, 95(9), 1845-1857 (2018), http://dx.doi.org/10.1080/00207160.2017.1343471.
[96] S. Arshad, D. Baleanu, J.F. Huang, M. M Al Qurashi, Y.F. Tang & Y. Zhao, Finite difference method for time-space fractional advection-diffusion equations with Riesz derivative, Entropy, 20(5), 321 (2018), https://www.mdpi.com/1099-4300/20/5/321.
[97] Z.G. Shi, Y.M. Zhao, F.W. Liu, F.L. Wang & Y.F. Tang, Nonconforming quasi-Wilson finite element method for 2D time fractional diffusion-wave equation on regular and anisotropic meshes, Applied Mathematics and Computation, 338, 290-304 (2018), https://doi.org/10.1016/j.amc.2018.06.026.
[98] Y.B. Wei, Y.M. Zhao, Y.F. Tang, F.L. Wang, Z.G Shi & K.Y. Li, High accuracy analysis of FEM for two-term mixed time-fractional diffusion-wave equations, Scientia Sinica Informationis, 48(7), 871-887 (2018), http://doi.org/10.1360/N112017-00295.
[99] S. Arshad, D. Baleanu, J.F. Huang, Y.F. Tang & Y. Zhao, Fourth order finite difference method for time-space fractional diffusion equations, EAJAM (East Asian Journal on Applied Mathematics), 8(4), 764-781 (2018), http://dx.doi.org/10.4208/eajam.280218.210518.
[100] Y.B. Wei, Y.M. Zhao, Z.G. Shi, F.L. Wang & Y.F. Tang, Spatial high accuracy analysis of FEM for two-dimensional multi-term time-fractional diffusion-wave equations, Acta Mathematicae Applicatae Sinica, English Series, 34(4), 828-841 (2018), https://10.1007/s10255-018-0795-1.
[101] J.F. Huang, Y. Zhao, S. Arshad, K.Y. Li & Y.F. Tang, Alternating direction implicit schemes for the two-dimensional time fractional nonlinear super-diffusion equations, Journal of Computational Mathematics, 37(3), 297-315 (2019), http://dx.doi.org/10.4208/jcm.1802-m2017-0196.
[102] H. Chen, X.H. Hu, R.J. Ren, T. Sun & Y.F. Tang, $L1$ Scheme on Graded Mesh for the Linearized Time Fractional KDV Equation with Initial Singularity, International Journal of Modeling, Simulation, and Scientific Computing (IJMSSC), 10(1), 1941006, (2019), https://doi.org/10.1142/S179396231941006X.
[103] J.F. Huang, S. Arshad, Y.D. Jiao, & Y.F. Tang, Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations, EAJAM (East Asian Journal on Applied Mathematics), 9(3), 538-557 (2019), https://doi.org/10.4208/eajam.230718.131018.
[104] S. Arshad, D. Baleanu & Y.F. Tang, Fractional differential equations with bio-medical applications, in Handbook of Fractional Calculus with Applications, Volume 7, Applications in Engineering, Life and Social Sciences, Part A (Edited by D. Baleanu & A. Mendes Lopes), pp. 1-20, Berlin, Boston: De Gruyter, (2019), https://doi.org/10.1515/9783110571905-001.
[105] Y.M. Zhao, F.L. Wang, X.H. Hu, Z.G. Shi & Y.F. Tang, Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on $2$D bounded domain, Computers & Mathematics with Applications, 78(5), 1705-1719 (Sept 1, 2019), https://doi.org/10.1016/j.camwa.2018.11.028.
[106] F.L. Wang, Y.M. Zhao, C. Chen, Y.B. Wei & Y.F. Tang, A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficients, Computers & Mathematics with Applications, 78(5), 1288-1301 (Sept 1, 2019), https://doi.org/10.1016/j.camwa.2018.11.029.
[107] B.B. Zhu, Y.F. Tang, R.L. Zhang & Y.H. Zhang, Symplectic Simulation of Dark Solitons Motion for Nonlinear Schrodinger Equation, Numerical Algorithms, 81(4), 1485-1503 (August, 2019), https://doi.org/10.1007/s11075-019-00708-8.
[108] R.L. Zhang, J. Liu, H. Qin & Y.F. Tang, Energy-preserving algorithm for gyrocenter dynamics of charged particles, Numerical Algorithms, 81(4),
1521-1530 (August, 2019), https://doi.org/10.1007/s11075-019-00739-1.
[109] F.L. Wang, Y.M. Zhao,
Z.G. Shi, Y.H. Shi & Y.F. Tang, High Accuracy Analysis of an Anisotropic
Nonconforming Finite Element Method
for Two-Dimensional Time Fractional Wave Equation, East Asian Journal on Applied Mathematics, 9(4), 797-817 (2019), https://doi.org/10.4208/eajam.260718.060119.
[110] X.B. Tu, A. Murua & Y.F. Tang, Construction of high order symplectic integrators via generating functions technique with its application in many-body problem, BIT Numerical Mathematics, 60, 509-535 (2019), https://doi.org/10.1007/s10543-019-00785-0.
[111] T.S. Aleroev, H.T. Aleroeva, O.A. Kovalchuk & Y.F. Tang, On the main oscillational properties of fractional differential equations, Georgian Mathematical Journal, 27(2), 177-182 (2020), https://doi.org/10.1515/gmj-2018-0072.
[112] W.P. Bu, L. Ji, Y.F. Tang &
J. Zhou, Space-time finite element method for the distributed-order time
fractional reaction diffusion equations,
Applied Numerical Mathematics, 152, 446-465 (2020), https://doi.org/10.1016/j.apnum.2019.11.010.
[113] L. Barletti, L. Brugnano, Y.F. Tang & B.B. Zhu, Spectrally accurate space-time solution of Manakov systems, Journal of Computational and Applied Mathematics, 377, 112918 (2020), 15 October 2020, https://doi.org/10.1016/j.cam.2020.112918.
[114] S. Arshad, T. Akman, D. Baleanu & Y.F. Tang, The Role of Obesity in Fractional Order Tumor-Immune Model, U.P.B. Sci. Bull., Series A, 82(2), 181-196 (2020), https://www.scientificbulletin.upb.ro/rev$_-$docs$_-$arhiva/rez6c8$_-$361078.pdf.
[115] P.Z. Jin, L. Lu, Y.F. Tang & G.E. Karniadakis, Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness, Neural Networks, 130, October, 85-99 (2020), https://doi.org/10.1016/j.neunet.2020.06.024.
[116] A.Q. Zhu, P.Z. Jin & Y.F. Tang, Deep Hamiltonian networks based on symplectic integrators (in Chinese), Mathematica Numerica Sinica, 42(3), 370-384 (2020), http://www.computmath.com/Jwk$_-$jssx/CN/article/showVolumnArticle.do?nian=2020\&juan=42\#, and https://arxiv.org/abs/2004.13830 for English version.
[117] Y.H. Shi, Y.M. Zhao, F.L. Wang & Y.F. Tang, Superconvergence analysis of FEM for 2D multi-term time fractional diffusion-wave equations with variable coefficient, International Journal of Computer Mathematics, 97(8), 1621-1635 (2020), https://doi.org/10.1080/00207160.2019.1639676.
[118] P.Z. Jin, Z. Zhang, A.Q. Zhu, Y.F. Tang & G.E. Karniadakis, SympNets: Intrinsic structure-preserving symplectic networks for
identifying Hamiltonian systems, Neural Networks, 132, December, 166-179 (2020), https://doi.org/10.1016/j.neunet.2020.08.017.
[119] Y. Zhao, C. Shen, M. Qu, W.P Bu & Y.F. Tang, Finite element methods for fractional diffusion equations, International Journal of Modeling, Simulation, and Scientific Computing, 11(4), 2030001 (2020), https://doi.org/10.1142/S1793962320300010.
[120] P.Z. Jin, Y.F. Tang & A.Q. Zhu, Unit triangular factorization of the matrix symplectic group, SIAM Journal on Matrix Analysis and Applications, 41(4), 1630-1650 (2020), https://doi.org/10.1137/19M1308839, https://arxiv.org/abs/1912.10926.
[121] Y.B. Wei, Y.M. Zhao, F.L. Wang, Y.F. Tang & J.Y. Yang, Superconvergence Analysis of Anisotropic FEMs for Time Fractional Variable Coefficient Diffusion Equations, Bulletin of the Malaysian Mathematical Sciences Society, 43, 4411-4429 (2020), https://doi.org/10.1007/s40840-020-00929-4. [122] J.F Huang, J.N. Zhang, S. Arshad & Y.F. Tang, A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations, Applied Numerical Mathematics, 159, 159-173 (2021), https://doi.org/10.1016/j.apnum.2020.09.003.
[123] H.J. Fan, Y.M. Zhao, F.L. Wang, Y.H. Shi & Y.F. Tang, A Superconvergent Nonconforming Mixed FEM for Multi-Term Time-Fractional Mixed Diffusion and Diffusion-Wave Equations with Variable Coefficients, East Asian Journal on Applied Mathematics, 11(1), 63-92 (2021), https://doi.org/10.4208/eajam.180420.200720.
[124] J.N. Zhang, T.S. Aleroev, Y.F. Tang & J.F. Huang, Numerical Schemes for Time-Space Fractional Vibration Equations, Advances in Applied Mathematics and Mechanics, 13, 806-826 (2021), https://doi.org/10.4208/aamm.OA-2020-0066.
[125] J.F. Huang, Z. Qiao, J.N. Zhang, S. Arshad & Y.F. Tang, Two linearized schemes for time fractional nonlinear wave equations with fourth-order derivative, Journal of Applied Mathematics and Computing, 66, 561-579 (2021), https://doi.org/10.1007/s12190-020-01449-x.
[126] J.F Huang, J.N. Zhang, S. Arshad & Y.F. Tang, A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity, Numerical Methods for Partial Differential Equations, 37, 2833-2848 (2021), 22 January 2021, https://doi.org/10.1002/num.22773.
[127] S. Arshad, I. Saleem, O. Defterli, Y.F. Tang & D. Baleanu, Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model, Physica Scripta, 96, 124029 (2021), 7 September 2021, https://iopscience.iop.org/article/10.1088/1402-4896/ac1e5a.
[128] J.N. Zhang, J.F. Huang, T.S.
Aleroev & Y.F. Tang, A Linearized ADI for Two-Dimensional Time-Space
Fractional Nonlinear Vibration Equations,
International Journal of Computer
Mathematics, 98(12), 2378-2392 (2021),
https://doi.org/10.1080/00207160.2021.1897113.
[129] A.Q. Zhu, P.Z. Jin & Y.F.
Tang, Approximation capabilities of measure-preserving neural networks, Neural Networks, 147, 72-80 (2022),
https://doi.org/10.1016/j.neunet.2021.12.007,
http://arxiv.org/abs/2009.01058, http://arxiv.org/abs/2106.10911.
[130] B.B. Zhu, Y.F. Tang & J. Liu, Energy preserving methods for guiding center system based on averaged vector field, Physics of Plasmas, 29, 032501 (2022), https://doi.org/10.1063/5.0075321.
[131] Y. Zhao, Z.P Mao, L. Guo, Y.F. Tang & G.E. Karniadakis, A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition, Journal of Computational Physics, 461, 111213 (2022), https://doi.org/10.1016/j.jcp.2022.111213.
[132] A.Q. Zhu, P.Z. Jin, B.B. Zhu & Y.F. Tang, On Numerical Integration in Neural Ordinary Differential Equations, Proceedings of the 39th International Conference on Machine Learning, PMLR 162, 27527-27547 (2022), https://proceedings.mlr.press/v162/zhu22f.html.
[133] H. Chen, M.Y. Chen, T. Sun \& Y.F. Tang, Local error estimate of L1 scheme for linearized time fractional KdV equation with weakly singular solutions, Applied Numerical Mathematics, 179, 183-190 (2022), https://doi.org/10.1016/j.apnum.2022.04.021.
[134] J.N. Zhang, Y.F. Tang & J.F. Huang, A fast Euler-Maruyama method for fractional stochastic differential equations, Journal of Applied Mathematics and Computing, (2022), https://doi.org/10.1007/s12190-022-01705-2.
[135] A.Q. Zhu, B.B. Zhu, J.W. Zhang, Y.F. Tang & J. Liu, VPNets: Volume-preserving neural networks for learning source-free dynamics, Journal of Computational and Applied Mathematics, 416, 114523 (2022), https://doi.org/10.1016/j.cam.2022.114523.
[136] J.F. Huang, Z.Y. Huo, J.N. Zhang & Y.F. Tang, An Euler-Maruyama Method and Its Fast Implementation for Multi-Term Fractional Stochastic Differential Equations, Mathematical Methods in Applied Sciences, (2022), https://doi.org/10.1002/mma.8594.