BIMSA

单位: 北京雁栖湖应用数学研究院 , 清华大学

邮箱: wayong@mail.tsinghua.edu.cn

研究方向: 应用偏微分方程的理论分析和数值方法

个人简介

雍稳安主要研究领域是偏微分方程、数值方法和非平衡态热力学。系统地建立了双曲偏微分方程松弛问题的数学理论（包括零松弛极限的存在稳定性，整体光滑解的存在性和长时间行为，Chapman-Enskog展开的有效性，边界条件的提法及其极限边界条件的导出，边界控制等），找到了这类问题的内在共性（Yong's stability condition）。创立了非平衡态热力学的守恒耗散理论（CDF），并成功地应用于生物、地学等领域，提出了已被实验验证的描述可压缩粘弹性流体流动的数学模型（Yong's model）。在计算流体力学方面，证明了工程上广泛使用的格子Boltzmann方法的稳定收敛性，并针对这种数值方法率先提出了单点边界格式（ZY method）, 已被广泛使用。主要结果发表在Arch. Rational Mech. Anal., Automatica, J. Comput. Phys., Philos. Trans. Royal Soc. A, Siam 系列等相关领域的知名国际刊物上，有些结果已被若干权威专著和教材所采纳。

研究兴趣

Mathematical Modeling, Machine Learning
Non-equilibrium Thermodynamics
Numerical Methods, Computational Fluid Dynamics
Applied Partial Differential Equations

教育经历

1989 - 1992 海德堡大学 博士 Dr.rer.nat.
1984 - 1987 中国科学院计算数学与科学工程计算研究所 硕士
1980 - 1984 中山大学 学士
- 2005 海德堡大学 Habilitation

工作经历

2021 - 北京雁栖湖应用数学研究院 Professor
2005 - 清华大学 荣誉教授
1998 - 2005 海德堡大学 Assistant Professor (C1)
1993 - 1998 海德堡大学 副研究员
1993 - 1993 苏黎世联邦理工学院 博士后
1987 - 1989 北京应用物理与计算数学研究所 助理教授

荣誉与奖项

2018 科学咨询委员会会员

出版物

[1] Zhiting Ma，Wen-An Yong, Non-relativistic limit of the Euler-$HMP_N$ approximation model arising in radiation hydrodynamics, Math. Meth. Appl. Sci., 46(2023), 13741-13780
[2] Qian Huang， Yihong Chen， Wen-An Yong, Discrete-velocity-direction models of BGK-type with minimum entropy: I. Basic idea, Journal of Scientific Computing, 95(2023), 3
[3] Juntao Huang, Yingda Cheng, Andrew J. Christlieb, Luke F. Roberts, and Wen-An Yong, Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures, Multiscale Modeling and Simulation, 21(2023), 2, 489-512
[4] Juntao Huang & Yizhou Zhou & Wen-An Yong, Data-driven discovery of multiscale chemical reactions governed by the law of mass action, J. Comput. Phys. 448:11 (2022), 110743.
[5] Yizhou Zhou & Wen-An Yong, Boundary conditions for hyperbolic relaxation systems with characteristic boundaries of type II, J. Differ. Equations 310:5 (2022), 198–234.
[6] Qian Huang & Julian Koellermeier & Wen-An Yong, Equilibrium Stability Analysis of Hyperbolic Shallow Water Moment Equations, Math. Meth. Appl. Sci., accepted on February 6, 2022.
[7] Xiaxia Cao & Wen-An Yong, Construction of Boundary Conditions for Hyperbolic Relaxation Approximations. II: Jin-Xin Relaxation Model, Quarterly of Applied Mathematics, accepted on April 28, 2022.
[8] YZ Zhou, W. Yong, Boundary conditions for hyperbolic relaxation systems with characteristic boundaries of type II, JOURNAL OF DIFFERENTIAL EQUATIONS, 310, 198-234
[9] XX Cao, WA Yong, CONSTRUCTION OF BOUNDARY CONDITIONS FOR HYPERBOLIC RELAXATION APPROXIMATIONS II: JIN-XIN RELAXATION MODEL, QUARTERLY OF APPLIED MATHEMATICS, DOI: 10.1090/qam/1627, Published Online, MAY 2022
[10] Fansheng Xiong, and Wen-An Yong, Learning stable seismic wave equations for porous media from real data, Geophysical Journal International, 230(2022), 1, 349-362
[11] Jin Zhao, Weifeng Zhao, Zhiting Ma, Wen-An Yong, and Bin Dong, Finding models of heat conduction via machine learning, International Journal of Heat and Mass Transfer(2022)
[12] Yizhou Zhou & Wen-An Yong, Boundary conditions for hyperbolic relaxation systems with characteristic boundaries of type I, J. Differ. Equations 281 (2021), 289–332.
[13] Pierre Lallemand & Li-Shi Luo & Manfred Krafczyk & Wen-An Yong, The lattice Boltzmann method for nearly incompressible flows, J. Comput. Phys. 431 (2021), 109713
[14] Weifeng Zhao & Juntao Huang & Wen-An Yong, Lattice Boltzmann method for stochastic convection-diffusion equations, SIAM J. UQ. 9:2 (2021), 536–563.
[15] Weifeng Zhao & Wen-An Yong, Boundary conditions for kinetic theory based models II. a linearized moment system, Math. Meth. Appl. Sci. 44:18 (2021), pp.14148-14172
[16] Wen-An Yong & Yizhou Zhou, Recent advances on boundary conditions for equations in nonequilibrium thermodynamics, Symmetry 13:9(2021), 1710. https://doi.org/10.3390/sym13091710
[17] Yong W A, Zhou Y. Recent Advances on Boundary Conditions for Equations in Nonequilibrium Thermodynamics[J]. Symmetry, 2021, 13(9): 1710.
[18] Huang J , Zhou Y , Yong W A . Data-driven discovery of multiscale chemical reactions governed by the law of mass action[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 448, 2021
[19] Juntao Huang, Zhiting Ma, Yizhou Zhou, and Wen-An Yong, Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-Equilibrium Flows, Journal of Non-Equilibrium Thermodynamics, 46(2021), 4, 355-370
[20] Qian Huang & Shuiqing Li & Wen-An Yong, Stability analysis of quadrature-based moment methods for kinetic equations, SIAM J. Appl. Math. 80:1 (2020), 206–231.
[21] Weifeng Zhao & Wen-An Yong, Boundary scheme for a discrete kinetic approximation of the Navier-Stokes equations, J. Sci. Comput. 82:3 (2020), UNSP 71.
[22] Wen-An Yong, Intrinsic properties of conservation-dissipation formalism of irreversible thermodynamics, Phil. Trans. R. Soc. A 378: 2170 (2020), 20190177.
[23] Jiawei Liu & Wen-An Yong & Jianxin Liu & Zhenwei Guo, Stable finite-difference methods for elastic wave modeling with characteristic boundary conditions, Mathematics 8:6 (2020), 1039.
[24] Jin Zhao & Zhimin Zhang & Wen-An Yong, Approximation of the multi-dimensional incompressible Navier-Stokes equations by discretevelocity vector-BGK models, J. Math. Anal. Appl. 486:2 (2020), 123901.
[25] Yizhou Zhou & Wen-An Yong, Construction of boundary conditions for hyperbolic relaxation approximations. I: the linearized Suliciu model, Math. Models and Methods Appl. Sci. 30:7 (2020), 1407–1439.
[26] Weifeng Zhao & Wen-An Yong, Weighted L2-stability of a discrete kinetic approximation for the incompressible Navier-Stokes equations on bounded domains, J. Comput. Appl. Math. 376 (2020), 112820.
[27] Wen-An Yong & Weifeng Zhao, Numerical analysis of the lattice Boltzmann method for the Boussinesq equations, J. Sci. Comput. 84:2 (2020),
[28] Jin Zhao & Zhimin Zhang & Wen-An Yong, Vector-type boundary schemes for the lattice Boltzmann method based on vector-BGK models, SIAM J. Sci. Comput. 42: 5(2020), 1250–1270.
[29] Wen-An Yong, Boundary stabilization of hyperbolic balance laws with characteristic boundaries, Automatica 101 (2019), 252–257.
[30] Weifeng Zhao & Juntao Huang & Wen-An Yong, Boundary conditions for kinetic theory based models I: lattice Boltzmann models, Multiscale Model. Simul. 17(2) (2019), 854-872.
[31] Weifeng Zhao & Wen-An Yong, Relaxation-rate formula for the entropic lattice Boltzmann model, Chin. Phys. B 28(11) (2019), 114701.
[32] Weifeng Zhao & Liang Wang & Wen-An Yong, On a tworelaxation-time D2Q9 lattice Boltzmann model for the Navier-Stokes equations, Physica A 492 (2018) 1570–1580.
[33] Vincent Giovangigli & Wen-An Yong, Volume Viscosity and Internal Energy Relaxation: Error Estimates, Nonlinear Analysis-Real World Applications 43 (2018), 213–244.
[34] Vincent Giovangigli & Zaibao Yang & Wen-An Yong, Relaxation Limit and Initial-Layers for a Class of Hyperbolic-Parabolic Systems, SIAM J. Math. Anal. 50 (2018), 4655–4697.
[35] Zaibao Yang, Wen-An Yong, Yi Zhu, Generalized hydrodynamics and the classical hydrodynamic limit(2018)
[36] Weifeng Zhao & Wen-An Yong, Single-node second-order boundary schemes for the lattice Boltzmann method, J. Comput. Phys. 329 (2017), 1–15.
[37] Weifeng Zhao & Wen-An Yong & Li-Shi Luo, Stability analysis of a class of globally hyperbolic moment systems, Commun. Math. Sci. 15:3 (2017), 609–633.
[38] Xiaokai Huo & Wen-An Yong, Global existence for viscoelastic fluids with infinite Weissenberg number, Commun. Math. Sci. 15:4 (2017), 1129–1140.
[39] Weifeng Zhao & Wen-An Yong, Maxwell iteration for the lattice Boltzmann method with diffusive scaling, Phys. Rev. E 95:3 (2017), 033311.
[40] Vincent Giovangigli & Wen-An Yong, Asymptotic stability and relaxation for fast chemistry fluids, Nonlinear Analysis-Theory Methods & Applications 159 (2017), 208–263.
[41] Yeping Li & Wen-An Yong, Zero Mach number limit of the compressible Navier-Stokes-Korteweg equations, Commun. Math. Sci. 14:1 (2016), 233–247.
[42] Jiawei Liu & Wen-An Yong, Stability analysis of the Biot/squirt models for wave propagation in saturated porous media, Geophysical Journal International 204 (2016), 535–543.
[43] Juntao Huang & Wen-An Yong & Liu Hong, Generalization of the Kullback-Leibler divergence in the Tsallis statistics, J. Math. Anal. Appl. 436 (2016), 501–512.
[44] Juntao Huang & Zexi Hu & Wen-An Yong, Second-order curved boundary treatments of the lattice Boltzmann method for convectiondiffusion equations, J. Comput. Phys. 310 (2016), 26–44.
[45] Michael Herty & Wen-An Yong, Feedback boundary control of linear hyperbolic systems with relaxation, Automatica 69 (2016), 12–17.
[46] Wen-An Yong & Weifeng Zhao & Li-Shi Luo, Theory of the lattice Boltzmann method: Derivation of macroscopic equations via the Maxwell iteration, Phys. Rev. E 93 (2016), 033310.
[47] Zexi Hu & Juntao Huang & Wen-An Yong, Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions,Phys. Rev. E 93 (2016), 043320.
[48] Xiaokai Huo & Wen-An Yong, Structural stability of a 1D compressible viscoelastic fluid model, J. Differ. Equations, 261:2 (2016), 1264–1284.
[49] Liu Hong & Chen Jia & Yi Zhu & Wen-An Yong, Novel dissipation properties of the master equation, J. Math. Phys. 57 (2016), 103303.
[50] Vincent Giovangigli & Wen-An Yong, Volume Viscosity and Internal Energy Relaxation: Symmetrization and Chapman-Enskog Expansion, Kinetic and Related Models, 8:1 (2015), 79–116.
[51] Zaibao Yang & Wen-An Yong, Validity of the Chapman-Enskog expansion for a class of hyperbolic relaxation systems, J. Differ. Equations 258:8 (2015), 2745–2766.
[52] Yi Zhu & Liu Hong & Zaibao Yang & Wen-An Yong, Conservationdissipation formalism of irreversible thermodynamics, J. Non-Equilib. Thermodyn. 40:2 (2015), 67–74.
[53] Yeping Li & Wen-An Yong, Quasi-neutral limit in a 3D compressible Navier-Stokes-Poisson-Korteweg model, IMA J. Appl. Math. 80:3(2015), 712–727.
[54] Juntao Huang & Hao Wu & Wen-An Yong, On initial conditions for the lattice Boltzmann method, Commun. Comput. Phys. 18:2(2015), 450–468.
[55] Liu Hong & Ya-Jing Huang & Wen-An Yong, A Kinetic Model for Cell Damage Caused by Oligomer Formation, Biophys. J. 109 (2015), 1338–1346.
[56] Juntao Huang & Wen-An Yong, Boundary conditions of the lattice Boltzmann method for convection-diffusion equations, J. Comput. Phys. 300 (2015), 70–91.
[57] Liu Hong & Zaibao Yang & Yi Zhu & Wen-An Yong, A novel construction of thermodynamically compatible models and its correspondence with Boltzmann-equation-based moment-closure hierarchies, J. Non-Equilib. Thermodyn. 40:4 (2015), 247–256.
[58] Yeping Li & Wen-An Yong, The zero Mach number limit of the three-dimensional compressible viscous magnetohydrodynamic equations, Chinese Ann. Math. B 36(6) (2015), 1043–1054.
[59] Yajing Huang & Liu Hong & Wen-An Yong, Partial equilibrium approximations in apoptosis. II. The Death-Inducing Signaling Complex Subsystem, Math. Biosci. 270 (2015), 126–134.
[60] Wen-An Yong, CFL condition, Boltzmann’s H-theorem, Onsager reciprocal relations and beyond, Math. Meth. Appl. Sci. 38:18 (2015), 4479–4486.
[61] Zaibao Yang, Wen-An Yong, Yi Zhu, A rigorous derivation of multicomponent diffusion laws(2015)
[62] Juntao Huang & Li Zhang & Wen-An Yong & Moran Wang, On complex boundary conditions of the lattice Boltzmann method for diffusion equations, Appl. Math. Mech. 35:3 (2014), 305–312 (in Chinese).
[63] Zaibao Yang & Wen-An Yong, Asymptotic analysis of the lattice Boltzmann method for generalized Newtonian fluid flows, Multiscale Model. Simul. 12:3 (2014), 1028–1045.
[64] Wen-An Yong, Newtonian limit of Maxwell fluid flows, Arch. Rational Mech. Anal. 214:3 (2014), 913–922.
[65] Liu Hong & Wen-An Yong, Simple moment-closure model for the self-assembling of breakable amyloid filaments, Biophys. J. 104 (2013), 533–540.
[66] Ya-Jing Huang & Wen-An Yong, Partial equilibrium approximations in apoptosis. I. The intracellular-signaling subsystem, Math. Biosci. 246 (2013), 27–37.
[67] Ya-Jing Huang & Wen-An Yong, A stable simplification of a Fassignaling pathway model for apoptosis, 2012 IEEE 6th International Conference on Systems Biology (ISB), 125–134.
[68] Hao Yan & Wen-An Yong, Stability of steady solutions to reactionhyperbolic systems for axonal transport, J. Hyper. Partial Differ. Eqns. 9:2 (2012), 325–337.
[69] Wen-An Yong, Conservation-dissipation structure of chemical reaction systems, Phys. Rev. E 86, 067101 (2012).
[70] Wen-An Yong & Li-Shi Luo, Accuracy of the viscous stress in the lattice Boltzmann equation with simple boundary conditions, Phys. Rev. E 86, 065701(R) (2012).
[71] Jiang Xu & Wen-An Yong, Zero-electron-mass Limit of Hydrodynamic Models for Plasmas, Proc. Roy. Soc. Edinburgh Sect. A 141:2(2011), 431–447.
[72] Jiang Xu & Wen-An Yong, A note on incompressible limit for compressible Euler equations, Math. Methods Appl. Sci. 34:7 (2011), 831–838.
[73] Hao Yan & Wen-An Yong, Weak entropy solutions of nonlinear reaction-hyperbolic systems for axonal transport, M3AS (Math. Models and Methods Appl. Sci.) 21:10 (2011), 2135–2154.
[74] Jiang Xu & Wen-An Yong, On the Relaxation-time Limits in the Bipolar Hydrodynamic Models for Semiconductors, In: Some Problems on Nonlinear Hyperbolic Equations and Applications, T. Li et al. (eds), World Scientific Publishing Company, 2010.
[75] Shuichi Kawashima & Wen-An Yong, Decay estimates for hyperbolic balance laws, ZAA (Zeitschrift f¨ur Analysis und ihre Anwendungen), 28 (2009), 1–33.
[76] Jiang Xu & Wen-An Yong, Relaxation-time Limits of Non-isentropic Hydrodynamic Models for Semiconductors, J. Differ. Equations, 247 (2009), 1777–1795.
[77] Jiang Xu & Wen-An Yong, Zero-relaxation Limit of Non-isentropic Hydrodynamic Models for Semiconductors, DCDS-A (Discrete and Continuous Dynamical Systems), 25:4 (2009), 1319–1332.
[78] Wen-An Yong, An Onsager-like relation for the lattice Boltzmann method, Computers & Mathematics with Applications, 58 (2009), 862–866.
[79] Michael Junk & Wen-An Yong, Weighted L2-stability of the lattice Boltzmann method, SIAM J. Numer. Anal., 47:3 (2009), 1651–1665.
[80] A. Dressel & Wen-An Yong, Traveling-wave solutions for hyperbolic systems of balance laws, In: Hyperbolic problems: theory, numerics, applications, S. Benzoni-Gavage et al. (eds), Springer, Berlin, 2008, 485–492.
[81] C. Rohde & N. Tiemann & Wen-An Yong, Weak and classical solutions for a model problem in radiation hydrodynamics, In: Hyperbolic problems: theory, numerics, applications, S. Benzoni-Gavage et al. (eds), Springer, Berlin, 2008, 891–899.
[82] Wen-An Yong, An interesting class of partial differential equations, J. Math. Phys. 49 (2008), 033503.
[83] Christian Rohde & Wen-An Yong, Dissipative entropy and global smooth solutions for radiation hydrodynamics and magnetohydrodynamics, M3AS (Mathematical Models and Methods in Applied Sciences), 18:12 (2008), 2151–2174.
[84] Christian Rohde & Wen-An Yong, The nonrelativistic limit in radiation hydrodynamics: I. weak entropy solutions for a model problem, J. Differ. Equations 234 (2007), 91–109.
[85] Yue-Jun Peng & Ya-Guang Wang & Wen-An Yong, Quasineutral limit of the nonisentropic Euler-Poisson system, Proc. R. Soc. Edinb. A 136A (5) (2006), 1013–1026.
[86] Alexander Dressel & Wen-An Yong, Existence of traveling wave solutions for hyperbolic systems of balance laws, Arch. Rational Mech. Anal. 182 (2006), 49–75.
[87] Wen-An Yong & Willi Jager, On hyperbolic relaxation problems, In: Analysis and Numerics for Conservation Laws, G. Warnecke (ed.), Springer, Berlin, 2005, 495–520.
[88] Wen-An Yong, A note on the zero Mach number limit of compressible Euler equations, Proc. Amer. Math. Soc. 133 (2005), 3079–3085.
[89] Yann Brenier & Wen-An Yong, Derivation of particle, string, and membrane motions from the Born-Infeld electromagnetism, J. Math. Phys. 46, 062305 (2005).
[90] Wen-An Yong & Li-Shi Luo, Nonexistence of H theorem for some lattice Boltzmann models, J. Stat. Phys. 121 (2005), 91–103.
[91] M. K. Banda & W.-A. Yong & A. Klar, A stability notion for lattice Boltzmann equations, SIAM J. Sci. Comput. 27 (2006), 2098–2111.
[92] Wen-An Yong, Entropy and global existence for hyperbolic balance laws, Arch. Rational Mech. Anal. 172 (2004), 247–266.
[93] Wen-An Yong, Diffusive relaxation limit of multidimensional isentropic hydrodynamical models for semiconductors, Siam J. Appl. Math. 64 (2004), 1737–1748.
[94] Shuichi Kawashima & Wen-An Yong, Dissipative structure and entropy for hyperbolic systems of balance laws, Arch. Rational Mech. Anal. 174 (2004), 345–364.
[95] M. K. Banda & W.-A. Yong & A. Klar, Stability structure for lattice Boltzmann equations: Some computational results, Proc. Appl. Math. Mech. 3 (2003), 72–75.
[96] Wen-An Yong & Li-Shi Luo, Nonexistence of H theorems for athermal lattice Boltzmann models with polynomial equilibria, Phys. Rev. E 67, 051105 (2003).
[97] Michael Junk & Wen-An Yong, Rigorous Navier-Stokes limit of the lattice Boltzmann equation, Asymptotic Anal. 35(2) (2003), 165–185.
[98] Wen-An Yong, Basic structures of hyperbolic relaxation systems, Proc. R. Soc. Edinb. 132A (2002), 1259–1274.
[99] Iuliu Sorin Pop & Wen-An Yong, A numerical approach to degenerate parabolic equations, Numer. Math. 92 (2002), 357–381.
[100] Wen-An Yong, Remarks on hyperbolic relaxation systems, In: Hyperbolic problems: theory, numerics, applications, Vols. I & II (Interna. Ser. Numer. Math. Vols. 140, 141 ), H. Freist¨uhler et al. (eds.), Birkh¨auser, Basel, 2001. 921–929.
[101] Wen-An Yong, Basic aspects of hyperbolic relaxation systems, in Advances in the Theory of Shock Waves, H. Freist¨uhler and A. Szepessy, eds., Progress in Nonlinear Differential Equations and Their Applications, Vol. 47, Birkh¨auser, Boston, 2001, 259–305.
[102] Corrado Lattanzio & Wen-An Yong, Hyperbolic-parabolic singular limits for first-order nonlinear systems, Commun. in Partial Differ. Equations 26 (5&6) (2001), 939–964.
[103] Hailiang Liu & Wen-An Yong, Time-asymptotic stability of boundarylayers for a hyperbolic relaxation system, Commun. in Partial Differ. Equations 26 (7&8) (2001), 1323–1343.
[104] Wen-An Yong & Kevin Zumbrun, Existence of relaxation shock profiles for hyperbolic conseration laws, Siam. J. Appl. Math. 60 (2000), 1565–1575.
[105] Iuliu Sorin Pop & Wen-An Yong, On the existence and uniqueness of a solution for an elliptic problem, Stud. Univ. Babes-Bolyai Math. 45 (2000), No. 4, 97–107.
[106] Wen-An Yong, Boundary conditions for hyperbolic systems with stiff source terms, Indiana Univ. Math. J. 48 (1999), 115-137.
[107] Wen-An Yong, Singular perturbations of first-order hyperbolic systems with stiff source terms, J. Differ. Equations 155 (1999), 89–132.
[108] Wen-An Yong, A simple approach to Glimm’s interaction estimates, Appl. Math. Lett. 12 (1999), 29-34.
[109] Wen-An Yong, A difference scheme for a stiff system of conservation laws, Proc. Roy. Soc. Edin. 128A (1998), 1403–1414.
[110] Wen-An Yong, Error analysis of difference methods for moving boundary problems of hyperbolic systems, Institut Mittag-Leffler (Stockholm), Report No. 6, 1997/98.
[111] Wen-An Yong, Existence and asymptotic stability of traveling wave solutions of a model system for reacting flow, Nonlinear Analysis: TMA, 26 (1996), 1791–1809
[112] Wen-An Yong, Numerical analysis of relaxation schemes for scalar conservation laws, IWR Preprint 95–30, Universit¨at Heidelberg, July 1995.
[113] Wen-An Yong, Singular perturbations of first-order hyperbolic systems, In: Nonlinear hyperbolic problems: theoretical, applied, and computational aspects (Notes Numer. Fluid Mech. Vol. 43), A. Donato et al. (eds.), Vieweg, Braunschweig, 1993, 597–604.
[114] Wen-An Yong, Explicit dissipative difference schemes for boundary problems of generalized Schr¨odinger systems, Acta Math. Appl. Sin. (English Ser.) 7 (1991), 173–186.
[115] Wen-An Yong & You-lan Zhu, Convergence of difference methods for nonlinear problems with moving boundaries, Sci. China (Series A) 33 (1990), 537–550.
[116] You-lan Zhu & Wen-An Yong, On stability and convergence of difference schemes for quasilinear hyperbolic initial-boundary-value problems, Lecture Notes in Mathematics, Vol. 1297, Springer, Berlin, 1987, 210–244.
[117] Wen-An Yong & You-lan Zhu, Stability of implicit difference schemes with space and time-dependent coefficients, J. Comp. Math. 5 (1987), 281–286.

更新时间: 2024-09-12 17:18:06