More Publications (selected after 1999)

  1. J. Xie, D. Liang, Z. Zhang, "Energy-preserving local mesh-refined splitting FDTD schemes for two dimensional Maxwell’s equations", J. Comput. Phys., 425, (2021), 109896.
  2. S. Sriskandarajah, D. Liang, H.M. Zhu, "Using the EC-S-FDTD Scheme to Approximate Eddy Currents Induced by Z-Gradient Coils", IEEE Trans. Antennas Propagat., DOI: 10.1109/TAP.2020.3048550, (2021).
  3. H.N. Kandel, D. Liang, "The mass-preserving solution-flux scheme for multi- layer interface parabolic equations", Appl. Numer. Math., 160 (2021), 42 - 64.
  4. Y. Shi, S.S. Xie, D. Liang, K. Fu, "High Order Compact Block-Centered Finite Difference Schemes for Elliptic and Parabolic Problems", J. Sci. Comput. 87 (2021), 86: 1-26.
  5. B. Hou, D. Liang, "Time fourth-order energy-preserving AVF finite difference method for nonlinear space-fractional wave equations", J. Comput. Appl. Math., 386 (2021), 113227.
  6. M. Sarai, D. Liang, "Even-Odd Cycled High-Order Splitting Finite Difference Time Domain Method for Maxwell's Equations", Int. J. Numeri. Anal. Modeling, 18 (2021), 79-99.
  7. Y.J. Yuan, D. Liang, "Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations", Adv. Appl. Math. Mech., 13 (2021), 1-17.
  8. B. Hou, D. Liang, "Energy-preserving time high-order AVF compact finite difference schemes for nonlinear wave equations with variable coefficients", J. Comput. Phys., 421, (2020), 109738.
  9. D. Liang, Z. Zhou, "The conservative splitting domain decomposition method for multicomponenet contamination flows in porous media", J. Comput. Phys., 400 (2020), 108974, 1-27.
  10. W. Xu, D. Liang, H.X. Rui, X. Li, "A multipoint flux mixed finite element method for Darcy-Forchheimer incompressible miscible displacement problem", J. Sci. Comput., 82 (2020), 2: 1-20.
  11. J. Xie, D. Liang, Z. Zhang, "Two novel energy dissipative difference schemes for the strongly coupled nonlinear space fractional wave equations with damping", Appl. Numer. Math., 157 (2020), 178 - 209.
  12. D. Deng, D. Liang, "The energy-preserving finite difference methods and their analyses for system of nonlinear wave equations in two dimensions", Appl. Numer. Math., 151 (2020), 172 - 198.
  13. M. Cui, F. Li, D. Liang, "High-order Characteristic-Finite Volume Methods For Aerosol Dynamic Equations", J. Comput. Appl. Math., 370 (2020), 112593, 1-16.
  14. Z. Zhang, D. Liang, Q. Wang, "Immersed finite element method and its analysis for parabolic optimal control problems with interfaces", Appl. Numer. Math., 147 (2020), 174-195.
  15. C.G. Chen, D. Liang, S.S. Xie, "The time high-order energy-preserving schemes for the nonlocal Benjamin-Ono equation", Int. J. Numer. Anal. Modeling , 17 (2020), 543 - 556.
  16. J.L. Wang, Y.S. Wang, D. Liang, "Construction of the Local Structure-Preserving Algorithms for the General Multi-Symplectic Hamiltonian System", Commun. Comput. Phys., 27 (2020), 828-860.
  17. K. Fu, D. Liang, "A Mass-Conservative Temporal Second Order and Spatial Fourth Order Characteristic FV Method for Atmospheric Pollution Advection Diffusion Problems", SIAM J. Sci. Comput., 41 (2019), B1178-B1210.
  18. W. Li, D. Liang, "The Energy Conservative Splitting FDTD scheme and its Energy Identities for Metamaterial Electromagnetic Lorentz System", Comput. Phys. Commun., 239 (2019), 94-111.
  19. B. Hou, D. Liang, H.M. Zhu, "The Conservative Time High-Order AVF Compact Finite Difference Schemes for Two-Dimensional Variable Coefficient Acoustic Wave Equations", J. Sci. Comput., 80 (2019), 1279-1309.
  20. Yousef Akhavan, D. Liang, M. Chen, "Second Order in Time and Space Corrected Explicit-Implicit Domain Decomposition Scheme for Convection-Diffusion Equations", J. Comput. Appl. Math., 357 (2019), 38-55.
  21. Hom N. Kandel, D. Liang, "The long wave fluid flows on inclined porous media with nonlinear Forchheimer's law", AIP Advances, 9 (2019), 095302: 1-21.
  22. Y. Gao, D. Liang, Y. Li, "Optimal weighted upwind finite volume method for convection-diffusion equations in 2D", J. Comput. Appl. Math., 359 (2019), 73-87.
  23. J.L. Wang, D. Liang, Y.S. Wang, "Analysis of a conservative high-order compact finite difference scheme for the Klein-Gordon-Schodinger equation", J. Comput. Appl. Math., 358 (2019), 84-86.
  24. B. Wang, T. Sun, D. Liang, "The conservative and fourth-order compact finite difference schemes for regularized long wave equation", J. Comput. Appl. Math., 356 (2019), 98-117.
  25. J. Xie, Z. Zhang, D. Liang, "A conservative splitting difference scheme for the fractional-in-space Boussinesq equation", Appl. Numer. Math., 143 (2019), 61-74.
  26. B. Hou, D. Liang, "A time second-order characteristic finite element method for nonlinear advection-di usion equations", Int. J. Numer. Anal. Modelling, 16 (2019), 276-296.
  27. J. Xie, Z. Zhang, D. Liang, "A new fourth-order energy dissipative difference method for high-dimensional nonlinear fractional generalized wave equations", Commum. Nonlinear Sci. Numer. Simul., 78 (2019), 104850, 1-21.
  28. D. Deng, J. Xie, Y. Jiang, D. Liang, "A second-order box solver for nonlinear delayed convection-diffusion equations with Neumann boundary conditions", Int. J. Computer Math., 96 (2019), 1879-1898.
  29. Z. Zhou, D. Liang, Y.S. Wong, "The new mass-conserving S-DDM scheme for two-dimensional parabolic equations with variable coefficients", Appl. Math. Comput., 338 (2018), 882-902.
  30. D. Deng, D. Liang, "The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations", Appl. Math. Comput., 329 (2018), 188-209.
  31. B. Wang, D. Liang, T.J. Sun, "The Conservative Splitting High-Order Compact Finite Difference Scheme for Two-Dimensional Schrodinger Equations", Int. J. Comput. Meths, 15 (2018), No.01, 1750079 (1-22).
  32. J.L. Wang, Y.S. Wang, D. Liang, "Analysis of a Fourier pseudo-spectral conservative scheme for the Klein–Gordon–Schrödinger equation", Int. J. Computer Math., 95 (2018), 36 - 60.
  33. J. Yan, Z. Zhang, T. Zhao, D. Liang, "High-order energy-preserving schemes for the improved Boussinesq equation", Numer. Methods Partial Diff. Eqns., 34 (2018), 1145-1165.
  34. K. Fu, D. Liang, "The Time Second Order Mass Conservative Characteristic FDM for Advection-Diffusion Equations in High Dimensions", J. Sci. Comput., 73 (2017), 26 - 49.
  35. Z. Zhou, D. Liang, "The mass-preserving and modified-upwind splitting DDM scheme for time-dependent convection-diffusion equations", J. Comput. Appl. Math., 317 (2017), 247 - 273.
  36. W. Li, D. Liang, Y.P. Lin, "Global energy-tracking identities and global energy-tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three-dimensional metamaterials", Numer. Methods Part. Diff. Eqns. , 33 (2017), 763 - 785.
  37. Y.J. Yuan, D. Liang, H.M. Zhu, "Optimal control of groundwater pollution combined with source abatement costs and taxes", J. Comput. Sci., 20 (2017), 17 - 29.
  38. W. Xu, D. Liang, and H. Rui, "A multipoint flux mixed finite element method for the compressible Darcy-Forchheimer models", Appl. Math. Comput. , 315 (2017), 259 - 277.
  39. D. W. Deng, Y. Jiang and D. Liang, "High-order finite difference methods for a second order dual-phase-lagging models of microscale heat transfer", Appl. Math. Comput., 309 (2017), 31 - 48.
  40. Y.J. Yuan and D. Liang, "Numerical Optimal Pollution Control Subject to The Convection Diffusion Transport Equations", Int. J. Numer. Anal. Modeling, 14 (2017), 437 - 455.
  41. Z. Zhou, D. Liang, "A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations", Adv. Appl. Math. Mech., 9 (2017), 795 - 817.
  42. J. Yan, Q. Zhang, Z. Zhang and D. Liang, "A new high-order energy-preserving scheme for the modified Korteweg-de Vries equation", Numer. Algor., 74 (2017), 659 - 674.
  43. K. Fu and D. Liang, "The conservative characteristic FD methods for atmospheric aerosol transport problems", J. Comput. Phys., 305 (2016), 494 - 520.
  44. D. Liang, K. Fu and W. Wang, "Modelling multi-component aerosol transport problems by the efficient splitting characteristic method", Atmos. Environ., 144 (2016), 297 - 314.
  45. W. Li and D. Liang, "Symmetric energy-conserved S-FDTD scheme for two-dimensional Maxwell's equations in negative index metamaterials", J. Sci. Comput. , 69 (2016), 696 - 735.
  46. Z. Zhou and D. Liang, "The mass-preserving S-DDM scheme for two-dimensional parabolic equations", Commun. Comput. Phys., 19 (2016), 411 - 441.
  47. W. Li, Y. Zhang, Y.S. Wong and D. Liang, "ADI-FDTD method for two-dimensional transient electromagnetic problem", Commun. Comput. Phys., 19 (2016), 94 - 123.
  48. M. Cui, Y. Su, D. Liang, "High-order Finite Volume Methods for Aerosol Dynamic Equations", Adv. Appl. Math. Mech., 8 (2016), 213 - 235.
  49. K. Fu, D. Liang, et al., "The time second-order characteristic FEM for nonlinear multicomponent aerosol dynamic equations in environment", Int. J. Numer. Anal. Modelling, 12 (2015), 211 - 229.
  50. W. Li and D. Liang, "Analysis of the energy-conserved S-FDTD scheme for variable coefficient Maxwell's equations in disk domains", Math. Methods Appl. Sci., (published online), (2015)
  51. J. Lou, H. Zhou, D. Liang, et al., "The Coupled Within- and Between-Host Dynamics in the Evolution of HIV/AIDS in China", J. Appl. Anal. Comput., 5 (2015), 731 - 750.
  52. S.H. Zhang and D. Liang, "LOD-ASEI and LOD-ASCN methods for two-dimension parabolic equations", Int. J. Computer Math., 92 (2015), 513 - 531.
  53. D. Liang and C. Du, "The Efficient S-DDM Scheme and its Analysis for Solving Parabolic Equations", J. Comput. Phys., 272 (2014), 46 - 69.
  54. M. Cui, K. Fu, D. Liang, et al., "Numerical analysis of the second-order characteristic FEM for nonlinear aerosol dynamic equations", J. Comput. Appl. Math., 261 (2014), 48-61.
  55. F. Zeng, H. Ma and D. Liang, "Energy-conserved splitting spectral methods for two dimensional Maxwell's equations", J. Comput. Appl. Math., 265 (2014), 301 - 321.
  56. Y. Akhavan, M. Chen, D. Liang, "Global Optimization of Total Power Generated from Wind Farm", POWERCON2014: The 2014 International Conference on Power System Technology, IEEE publisher, ISBN: 978-1-4799-5032-4, (2014), 2945-2950.
  57. D. Liang and Q. Yuan, "The spatial fourth-order energy-conserved S-FDTD scheme for Maxwell's equations", J. Comput. Phys., 243 (2013), 344 - 364.
  58. F. Gao and D. Liang, "A new weighted upwind finite volume element method based on non-standard covolume for time-dependent convection diffusion problems", Int. J. Numer. Meth. Fluids, 73 (2013), 953 - 975.
  59. W. Li, D. Liang and Y. Lin, "A new energy-conserved S-FDTD scheme for Maxwell's equations in metamaterials", Int. J. Numer. Anal. Modelling, 10 (2013), 775 - 794.
  60. D. Liang, P. Weng and J. Wu, "Traveling Wave Solutions in A Delayed Predator-Prey Diffusion PDE System: Point-to-Periodic and Point-to-Point Waves", IMA J. Appl. Math., 77 (2012), 516-545.
  61. L. Gao and D. Liang, "New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D", Commun. Comput. Phys., 11 (2012), 1673 - 1696.
  62. K. Fu, D. Liang, W. Wang, Y. Cheng, S. Gong, "Multi-component atmospheric aerosols prediction by a multi-functional MC-HDMR approach", Atmos. Res., 113 (2012), 43-56.
  63. Q. Yuan and D. Liang, "A New Multiple Sub-domain RS-HDMR Method and its Application to Tropospheric Alkane Photochemistry Model", Int. J. Numer. Anal. Modeling, Ser. B, 2 (2011), 73 - 90.
  64. Frank X. Yu, W. Weng, P. Taylor and D. Liang,"Relaxation Factor Effects in the Non-Linear Mixed Spectral Finite Difference Model of Flow over Topographic Features", Boundary-Layer Meteorology, 140 (2011), 23 - 35.
  65. D. Liang, G. Sun and W. Wang, "Second order characteristic schemes in time and age for a nonlinear age-structured population model", J. Comput. Appl. Math., 235 (2011), 3841-3858.
  66. C. Du and D. Liang,"An Efficient S-DDM Iterative Approach for Compressible Contamination Fluid Flows in Porous Media", J. Comput. Phys., 229 (2010), 4501-4521.
  67. W. Chen, X. Li and D. Liang, "Energy-conserved Splitting Finite Difference Time Domain Methods for Maxwell's Equations in Three Dimensions", SIAM J. Numer. Anal., 48 (2010), 1530-1554.
  68. Y. Cheng, D. Liang, W. Wang, S. Gong and M. Xue, "An Efficient Approach of Aerosol Thermodynamic Equilibrium Predictions by the HDMR Method", Atmos. Environ., 44 (2010), 1321-1330.
  69. D. Liang and C. Du, "An Efficient Splitting Domain Decomposition Approach for Parabolic-type Time-dependent Problems in Porous Media", High Performance Computing and Applications, Lecture Notes in Computer Sci. 5938, (Springer), (2010), 69-77.
  70. D. Liang, W. Wang and Y. Cheng, "An Efficient Second Order Characteristic Finite Element Method for Nonlinear Aerosol Dynamic Equations", Int. J. Numer. Methods Engng., 80 (2009), 338 - 354.
  71. M. Zivkovic Gojovic, D. Liang and J. Wu, "Structured Influenza Model for Meta-population", Int. J. Biomath., 2 (2009), 525 - 541.
  72. G. Sun, D. Liang and W. Wang, "Numerical analysis to discontinuous Galerkin methods for the age structured population model of marine invertebrates", Numer. Methods Partial Diff. Eqns., 25 (2009), 470 - 493.
  73. D. Liang, Q. Guo and S. Gong, "Wavelet Galerkin Methods for Aerosol Dynamic Equations in Atmospheric Environment", Commun. Comput. Phys., 6 (2009), 109 - 130.
  74. Thomas Y. Hou and D. Liang, "Multiscale analysis for convection dominated transport equations", Dis. Cont. Dyn. Sys., Ser. A, 23 (2009), 281 - 298.
  75. W. Chen, X. Li and D. Liang, "Symmetric Energy-Conserved Splitting FDTD Scheme for the Maxwell's Equations", Commun. Comput. Phys., 6 (2009), 804 - 825.
  76. D. Liang, Q. Guo and S. Gong, "A New Splitting Wavelet Method for Solving the General Aerosol Dynamics Equation, J. Aerosol Sci., 39 (2008), 467-487.
  77. W. Chen, X. Li and D. Liang, "Energy-conserved splitting FDTD methods for Maxwells equations", Numerische Mathematik, 108 (2008), 445 - 485.
  78. P. Weng, D. Liang and J. Wu, "Asymptotic Patterns of a Structured Population Diffusing in a Two-Dimensional Strip", Nonlinear Anal. - Theory Methods and Applications, 69 (2008), 3931-3951.
  79. L. Gao, B. Zhang and D. Liang, "Splitting Finite Difference Methods on Staggeres Grids for Three-Dimensional Time-Dependent Maxwell Equations", Commun. Comput. Phys., 4 (2008) 405 - 432.
  80. D. Liang, C. Du and H. Wang, "A Fractional Step ELLAM Approach to High-Dimensional Convection-Diffusion Problems with Forward Particle Tracking", J. Comput. Phys., 221 (2007), 198 - 225.
  81. M. Gardam, D. Liang, S.M. Moghadas, J. Wu, Q. Zeng and H. Zhu, "The Impact of Prophylaxis of Healthcare Workers on Influenza Pandemic Burden", J. Royal Soc. Interf., 4 (2007), 727 - 734.
  82. S. Wang, D. Liang, X. Feng and L. Ye, "A Derivative Free Optimization Algorithm based Conditional Moments", J. Math. Anal. Appl., 331 (2007), 1337-1360.
  83. L. Gao, B. Zhang and D. Liang, "The Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations in Two Dimensions", J. Comput. Appl. Math., 205 (2007), 207 - 230.
  84. D. Liang and W. Zhao, "An Optimal Weighted Upwinding Covolume Method on Nonstandard Grids for Convection-Diffusion Problems in 2D", Int. J. Numer. Methods Engng., 67 (2006), 553-577.
  85. D. Liang, H. Wang and R.C. Sharpley, "Finite Element Approximations to One Phase Nonlinear Free Boundary Problem in Groundwater Contamination Flow", Numer. Methods Partial Diff. Eqns., 22 (2006), 1268-1288.
  86. N. Vaidya H. Huang and D. Liang, "Grown-in Defects Modelling of InSb Crystals and Computation", Commun. Comput. Phys., 1 (2006), 511 - 527.
  87. D. Liang, J. Wu and F. Zhang, "Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions", Math. Biosci. Engng., 2 (2005), 111-132.
  88. D. Liang and B. Zhang, "Numerical Analysis of Graded Mesh Methods for a Class of Second Kind Integral Equations on the Real Line", J. Math. Anal. Appl., 294 (2004), 482-502.
  89. H. Huang, D. Liang and B. Wetton, "Computation of a Moving Drop/Bubble on a Solid Surface Using a Front-Tracking Method", Commun. Math. Sci., 2 (2004), 535-552.
  90. L.P. Gao, D. Liang and B. Zhang, "Error Estimates for Mixed Finite Element Approximations of the Viscoelasticity Wave Equation", Math. Methods Appl. Sci., 27 (2004), 1997-2016.
  91. D. Liang and W. Zhao, "The Weighted Upwinding Finite Volume Method for the Convection-Diffusion Problem on a Nonstandard Covolume Grid", Appl. Numer. Anal. Comput. Math., 1 (2004), 180-194.
  92. D. Liang and J. Wu, "Travelling Waves and Numerical Approximations in a Reaction Advection Diffusion Equation with Non-local Delayed Effects", J. Nonlinear Sci., 13 (2003), 289-310.
  93. H. Wang, D. Liang, R.E. Ewing, S. L. Lyons and G. Qin, "An Improved Numerical Simulator for Compressible Flows in Porous Media", Numer. Methods Partial Diff. Eqns., 19 (2003), 343-362.
  94. D. Liang, "Upwinding Finite Covolume Methods for Unsteady Convection-Diffusion Problems", Contemp. Math. 329, American Mathematical Society, (2003), 245-252.
  95. H. Wang, D. Liang, R.E. Ewing, S. L. Lyons and G. Qin, "An ELLAM approximation for highly compressible multicomponent flows in porous media", Comput. Geosci., 6 (2002), 227-251.
  96. W. Zhao and D. Liang, "Modified High-Order Upwind Methods for Convection Diffusion Problems", Acta Math. Appl. Sinica, (Springer), 18 (2002), 131-146.
  97. Y.R. Yuan, D. Liang and H. Rui, "Numerical Predicting the Consequences of Seawater Intrusion and Protection Projects", Appl. Math. Mech., (Kluwer Academic), 22 (2001), 1291-1300.
  98. H. Wang, D. Liang, R.E. Ewing, S. L. Lyons and G. Qin, "An Approximation to Miscible Displacement in Porous Media with Point Sources and Sinks by an Eulerian-Lagrangian Localized Adjoint Method and Mixed Finite Element Methods", SIAM J. Sci. Comput., 22 (2000), 561-581.
  99. H. Wang, D. Liang, R.E. Ewing, S. L. Lyons and G. Qin, "An ELLAM-MFEM Solution Technique for Compressible Fluid Flow in Porous Media with Point Sources and Sinks", J. Comput. Phys., 159 (2000), 344-376.
  100. H. Wang, D. Liang, R. E. Ewing, S. L. Lyons and G. Qin, "An Accurate Approximation to Compressible Flow in Porous Media with Wells", Numerical Treatment of Multiphase Flows in Porous Media, Lecture Notes in Phys. 552, Springer-Verlag, Berlin, (2000), 324-332.
  101. D. Liang and B. Zhang, "A Finite Element Method for a Unidimensional Single-Phase Nonlinear Free Boundary Problem in Groundwater Flow", IMA J. Numer. Anal., 19 (1999), 563-579.