List of Publications
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Dianming Hou and Chuanju Xu,
Robust and stable schemes for time fractional molecular beam epitaxial growth model using SAV approach,
Journal of Computational Physics,
2021, 445, p110628.
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Hui Yao, Mejdi Azaiez, and Chuanju Xu,
New Unconditionally Stable Schemes for the Navier-Stokes Equations,
Communications in Computational Physics,
2021, 30, p1083-1117.
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Bin Fan and Chuanju Xu,
Inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems,
Inverse Problems,
2021, 37(4), p045007.
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Enze Shi and Chuanju Xu,
A comparative investigation of neural networks in solving differential equations,
Journal of Algorithms & Computational Technology,
2021, 15, 1748302621998605.
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Dianming Hou, Hongyi Zhu, and Chuanju Xu,
Highly efficient schemes for time-fractional Allen-Cahn equation using extended SAV approach,
Numerical Algorithms,
2021, 88, p1077-1108.
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Xingyang Ye and Chuanju Xu,
A posteriori error estimates of spectral method for the fractional optimal control problems with non-homogeneous initial conditions,
AIMS Mathematics,
2021, 6(11), p12028-12050.
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Bin Fan, Mejdi Azaiez, and Chuanju Xu,
An extension of the landweber regularization for a backward time fractional wave problem,
Discrete & Continuous Dynamical Systems-S,
2021, 14(8), 2893.
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Junying Cao, Zhiqiang Wang, and Chuanju Xu,
A High-Order Scheme for Fractional Ordinary Differential Equations with the Caputo-Fabrizio Derivative,
Communications on Applied Mathematics and Computation,
2020, 2(2), p179-199.
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Xiaolan Zhou, Mejdi Azaiez, and Chuanju Xu,
SAV Method Applied to Fractional Allen-Cahn Equation,
Spectral and High Order Methods for Partial Differential Equations
(ICOSAHOM 2018), Springer proceeding,
2020, 38(4), p489-500.
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M. T. Hasan and Chuanju Xu,
High order finite difference/spectral methods to a water wave model with nonlocal viscosity,
Journal of Computational Mathematics,
2020, 38(4), p580-605.
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Xingyang Ye, Shimin Lin, and Chuanju Xu,
Dynamical analysis of a fractional-order avian-human influenza epidemic model with logistic growth for avian population,
Journal of Algorithms & Computational Technology,
2020, 14, 1748302620966704.
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M. T. Hasan and Chuanju Xu,
The stability and convergence of time-stepping/spectral methods with asymptotic behaviour for the Rosenau-Burgers equation,
Applicable Analysis,
2020, 99(12), p2013-2025.
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Xiaolan Zhou, Mejdi Azaiez, and Chuanju Xu,
Reduced-Order Modelling for the Allen-Cahn Equation Based on Scalar Auxiliary Variable Approaches,
Journal of Mathematical Study,
2019, 52(3), p258-276.
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Dianming Hou, Yumin Lin, Mejdi Azaiez, Chuanju Xu,
A Muntz-Collocation Spectral Method for Weakly Singular Volterra Integral Equations,
Journal of Scientific Computing,
2019, 81(3), p2162-2187.
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Chuanju Xu,
Spectral methods for some kinds of fractional differential equations,
Handbook of Fractional Calculus with Applications, De Gruyter,
2019, 3, p101-126.
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Xingyang Ye and Chuanju Xu,
A fractional order epidemic model and simulation for avian influenza dynamics,
Mathematical Methods in the Applied Sciences,
2019, 42(14), p4765-4779.
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Hongyi Zhu and Chuanju Xu,
A Fast High Order Method for the Time-Fractional Diffusion Equation,
,
SIAM Journal on Numerical Analysis,
2019, 57(6), p2829-2849.
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Dianming Hou, Mejdi Azaiez, and Chuanju Xu,
Muntz Spectral Method for Two-Dimensional Space-Fractional Convection-Diffusion Equation,
Communications in Computational Physics,
2019, 26(5), p1415-1443.
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Dianming Hou, Mejdi Azaiez, and Chuanju Xu,
A variant of scalar auxiliary variable approaches for gradient flows,
Journal of Computational Physics,
2019, 395, p307-332.
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Xiaoling Liu, Fangying Song, and Chuanju Xu,
An Efficient Spectral Method for the Inextensible Immersed Interface in Incompressible Flows,
Communications in Computational Physics,
2019, 25(4), p1071-1096.
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Laurence Cherfils, Alain Miranville, Shuiran Peng, Chuanju Xu,
Analysis of discretized parabolic problems modeling electrostatic micro-electromechanical systems,
Discrete & Continuous Dynamical Systems-S,
2019, 12(6), p1601-1621.
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Chunwan Lv, M. Azaiez, and Chuanju Xu,
Spectral Deferred Correction Methods for Fractional Differential Equations,
Numerical Mathematics-Theory Methods and Applications,
2018, 11(4), p729-751.
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Dianming Hou, M. T. Hasan, and Chuanju Xu,
Muntz spectral methods for the time-fractional diffusion equation,
Computational Methods in Applied Mathematics,
2018, 18(1), p43-62.
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Shimin Lin, Mejdi Azaiez, and Chuanju Xu,
A fractional Stokes equation and its spectral approximation,
International journal of numerical analysis and modeling,
2018, 15(1-2), p170-192.
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Xiaojun Zhou and Chuanju Xu,
Analysis of a system of autonomous fractional differential equations,
International Journal of Biomathematics,
2017, 10(07), 1750094.
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Shimin Lin, Mejdi Azaiez, and Chuanju Xu,
Using PGD to Solve Nonseparable Fractional Derivative Elliptic Problems,
Springer Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119):
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM2016,
2017, p203-213.
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Fangying Song, Chuanju Xu, and GE Karniadakis,
Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations,
SIAM Journal on Scientific Computing,
2017, 39(4), pA1320-A1344.
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Xiaojun Zhou and Chuanju Xu,
Numerical Solution of the Coupled System of Nonlinear Fractional Ordinary Differential Equations,
Advances in Applied Mathematics and Mechanics,
2017, 9(3), p574-595.
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Xiaoling Liu and Chuanju Xu,
Efficient Time-Stepping/Spectral Methods for the Navier-Stokes-Nernst-Planck-Poisson Equations,
Communications in Computational Physics,
2017, 21(5), p1408-1428.
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Dianming Hou, M. Hassan, and Chuanju Xu
Muntz Spectral Methods for the Time-Fractional Diffusion Equation,
Computational Methods in Applied Mathematics,
2017, 18(1), p43-62.
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Dianming Hou and Chuanju Xu,
A fractional spectral method with applications to some singular problems,
Advances in Computational Mathematics,
2017, 43(5), p911-944.
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Tanzil Hasan Mohammad and Chuanju Xu,
Numerical approximation for MHD flows of generalized viscoelastic fluid,
Applicable Analysis, 2017, 1-19, 10.1080/00036811.2017.1397638.
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Fangying Song, Chuanju Xu, and George Em Karniadakis,
A fractional phase-field model for two phase
flows with tunable sharpness: Algorithms and simulations, Comput. Methods
Appl. Mech. Engrg. 2016, 305, p376-404.
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Shimin Lin and Chuanju Xu,
Theoretical and Numerical Investigation of Fractional Differential
Equations (in Chinese),
Mathematica Numerica Sinica, 2016, 38(1), p1-24.
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Xiaojun Zhou and Chuanju Xu,
Well-posedness of a kind of nonlinear coupled system of
fractional differential equations, SCIENCE CHINA Mathematics, 2016,
59(6), p1209-1220.
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Xingyang Ye and Chuanju Xu,
A spectral method for optimal control problems governed by
the abnormal diffusion equation with integral constraint on state (in Chinese),
SCIENCE CHINA Mathematics, 2016, 46(7), p1053-1070.
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Chunwan Lv and Chuanju Xu, Error analysis of a high order method for time-fractional
diffusion equations, SIAM J. Sci. Comput., 2016, 38(5), pA2699-A2724.
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Yanhui Su, Lizhen Chen, Xianjuan Li, and Chuanju Xu,
On the Inf-Sup Constant of a Triangular
Spectral Method for the Stokes Equations, Comput. Methods Appl. Math. 2016, DOI:
10.1515/cmam-2016-0011.
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Xianjuan Li, Tao Tang, and Chuanju Xu,
Numerical Solutions for Weakly Singular Volterra
Integral Equations Using Chebyshev and Legendre Pseudo-Spectral Galerkin Methods,
J Sci Comput, 2016, 67(1), p43-64.
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F.Y.Song and C.J.Xu,
Spectral direction splitting methods for two-dimensional space fractional
diffusion equations,
Journal of Computational Physics, 2015, 299(15), p196-214.
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Chunwan Lv and Chuanju Xu,
Improved error estimates of a finite difference/spectral method for
time-fractional diffusion equations,
International Journal of Numerical Analysis and Modeling, 2015, 12(2), p384-400.
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Xingyang Ye and Chuanju Xu,
A posteriori error estimates for the fractional optimal control problems,
Journal of Inequalities and Applications, 2015, 141, p1-13.
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Xingyang Ye and Chuanju Xu,
A space-time spectral method for
the time fractional diffusion optimal control problems,
Advances in Difference Equations,
2015:156, DOI 10.1186/s13662-015-0489-4.
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F.Y.Song, X.L. Liu, and C.J.Xu,
A Spectral Element Method for Human Carotid Atherosclerotic Plaques,
Chinese Journal of Engineering Mathematics, 2015(4), p546-556.
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Weiwei Wang and Chuanju Xu,
Spectral methods based on new formulations for coupled Stokes and Darcy equations,
Journal of Computational Physics, 2014, 257, p126-142.
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Jun Zhang and Chuanju Xu,
Finite difference/spectral approximations to a water wave model with a nonlocal viscous term,
Applied Mathematical Modelling, 2014, 38, p4912-4925.
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Lizhen Chen, Jie Shen, Chuanju Xu, and Lishi Luo,
Parallel spectral-element direction splitting method for incompressible Navier-Stokes equations,
Applied Numerical Mathematics, 2014, 84, p66-79.
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Junying Cao, Chuanju Xu, and Ziqiang Wang,
A high order finite difference/spectral approximations to the time fractional diffusion equations,
Advanced Materials Research, 2014, 875-877, p781-785.
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Xingyang Ye and Chuanju Xu,
A Spectral Method for Optimal Control Problems Governed by the Time Fractional Diffusion Equation with Control Constraints,
ICOSAHOM 2012,
Lecture Notes in Computational Science and Engineering, Springer, 2014, 95, p403-414.
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Lizhen Chen and Chuanju Xu,
A Time Splitting Space Spectral Element Method for the Cahn-Hilliard Equation,
East Asian Journal on Applied Mathematics, 2013, 3(4), p333-351.
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Xianjuan Li, Tao Tang, and Chuanju Xu,
Parallel in time algorithm with spectral-subdomain
enhancement for volterra integral equations, SIAM J. Numer. Anal, 2013, 51(3), p1735-1756.
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Junying Cao, Chuanju Xu,
A high order schema for the numerical solution of the ordinary fractional
differential equations,
Contemporary Mathematics, 2013, 586, http://dx.doi.org/10.1090/conm/586/11658.
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Junying Cao, Chuanju Xu,
A high order schema for the numerical solution of the fractional
ordinary differential equations,
Journal of Computational Physics, 2013, 238, p154-168.
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Xingyang Ye, Chuanju Xu,
Spectral Optimization Methods for the Time
Fractional Diffusion Inverse Problem,
Numer. Math. Theor. Meth. Appl., 2013, 6(3), p499-519.
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Dong Qu, Chuanju Xu,
Generalized Polynomial Chaos Decomposition and Spectral Methods for the
Stochastic Stokes Equations, Computers & Fluids,
2013, 71, p250-260.
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Lizhen Chen, Jie Shen, and Chuanju Xu,
A Unstructured Nodal Spectral-Element Method for
the Navier-Stokes Equations, Commun. Comput. Phys.,
2012, 12(1), p315-336.
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Yumin Lin, Xianjuan Li, and Chuanju Xu,
Finite Difference/Spectral Approximation for the Fractional Cable Equations, Mathematics of Computation,
2011, 80(275), p1369-1396.
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Lizhen Chen, Jie Shen, and Chuanju Xu,
A Triangular Spectral Method for the Stokes
Equations, Numer. Math. Theor. Meth. Appl.,
2011, 4(2), p158-179.
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Lizhen Chen, Jie Shen, and Chuanju Xu,
Spectral Direction Splitting Schemes for the
Incompressible Navier-Stokes Equations, East Asian Journal on Applied Mathematics,
2011, 1(3), p215-234.
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Claude-Michel Brauner, Luca Lorenzi, Gregory I. Sivashinsky, and Chuanju Xu,
On a Strongly Damped Wave Equation for the Flame Front, Chinese Annals of Mathematics,
2010, 31B(6), p819-840.
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Qingqu Zhuang, Chuanju Xu,
Legendre-Laguerre coupled spectral element methods for second- and
fourth-order equations on the half line, Journal of Computational and Applied Mathematics,
2010, 235, p615-630.
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Xianjuan Li and Chuanju Xu,
Existence and Uniqueness of the Weak Solution of
the Space-Time Fractional Diffusion Equation and a
Spectral Method Approximation, Commun. Comput. Phys., 2010, 8(5), p1016-1051.
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Dong Qu and Chuanju Xu,
Discrete variational adjoint assimilations for parameter optimizations via spectral methods,
Inverse Problems in Science and Engineering, 2010, 18(3), p417-436.
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Qingqu Zhuang, Jie Shen, and Chuanju Xu, A Coupled
Legendre-Laguerre Spectral-Element Method for the Navier-Stokes
Equations in Unbounded Domains, J. Sci. Comput., 2010,
42(1), p1-22.
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X.J.Li and C.J.Xu, A Finite Difference/Spectral Element Method for the Fractional Nernst-Planck Equation,
Chinese Journal of Engineering Mathematics (in Chinese), 2010,
27(2), p207-218.
- X.J.Li and C.J.Xu, A Space-Time Spectral Method for the Time
Fractional Diffusion Equation, SIAM J. Numer. Anal., 2009, 47(3),
p2108-2131.
- Zhijian Rong, Chuanju Xu,
Spectral Vanishing Viscosity for Large-Eddy Simulations by Spectral Element Methods,
Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(2), p155-161.
- Mejdi Azaiez, Jie Shen, Chuanju Xu, and Qingqu Zhuang,
A Laguerre-Legendre Spectral Method for the Stokes Problem in a Semi-Infinite Channel ,
SIAM J. Numer. Anal., 2008, 47(1), p271-292.
- Zhijian Rong, Chuanju Xu, Numerical approximation of acoustic waves
by spectral element methods,
Appl. Numer. Math., 2008, 58(2), p999-1016.
- Zhijian Rong, Chuanju Xu,
A P_N x P_N Spectral Element Projection Method for the Unsteady Incompressible Navier-Stokes Equations,
Numer. Math. Theor. Meth. Appl., 2008, 1, p275-296.
- Y.M.Lin, C.J.Xu, Finite difference/spectral approximations for the time-fractional diffusion equation,
J. Comput. Phys., 2007, 225(2), p1533-1552.
- C.J.Xu, Y.M.Lin, A numerical comparison of outflow boundary conditions for
spectral element simulations of incompressible flows,
Commun. Comput. Phys., 2007, 2, p477-500.
- L.Jiang, C.J.Xu, Spectral Element Viscosity Methods for Nonlinear Conservation
Laws on the Semi-Infinite Interval, Numer. Math. (J. Chinese Univ.), 2007, 16(2), p112-130.
- C.J.Xu, T.Tang, Stability Analysis of Large Time-Stepping Methods for Epitaxial Growth Models,
SIAM J. Numer. Anal. 2006, 44(4), p1759-1779.
- Q.Q.Zhuang, C.J.Xu, A Spectral Element/Laguerre Coupled Method
to the Elliptic Helmholtz Problem on the Half Line,
Numer. Math. (J. Chinese Univ.), 2006, 15(3), p193-208.
- C.J.Xu, Stabilization Methods for Spectral Element Computations of Incompressible Flows,
Journal of Scientific Computing, 2006, 27(1-3), p495-505.
- T.L.Hong, C.J.Xu, A MPI parallel preconditioned spectral element method for the
Helmholtz equation,
Numer. Math. (J. Chinese Univ.), 2005, 14(1), p56-66.
- F.H.Huang, C.J.Xu, On the error estimates for the rotational pressure-correction
projection spectral methods for the unsteady Stokes equations,
J. Comput. Math., 2005, 23(3), p285-304.
- C.J.Xu, R.Pasquetti, Stabilized spectral element computations of high Reynolds
number incompressible flows,
J. Comput. Phys., 2004, 196(2), p680-704.
- Y.M.Lin, C.J.Xu, A fractional step method for the unsteady viscous/inviscid
coupled equations, proceeding of SCA03,
Hong Kong City University, Sciences press, 2004.
- Y.M.Lin, C.J.Xu, A fractional step method for the time dependent
incompressible Navier-Stokes/Euler coupled equations, Acta Aerodynamica Sinica,
2003, 21(3), p368-376.
- R.Pasquetti, C.J.Xu, Note: Comments on Filter-Based
Stabilization of Spectral Element Methods,
J. Comput. Phys., 2002, 182, p646-650.
- R.Pasquetti, C.J.Xu, High-Order Algorithms for
Large-Eddy Simulation of incompressible Flows,
J. Scient. Computing, 2002, 17(1-3), p273-284.
- F.H.Huang, C.J.Xu, A spectral element method of the
viscous/inviscid coupled equations in complex geometries,
J.of Xiamen Univ., 2002, 41(3), p291-296.
- C.J.Xu, R.Pasquetti, On the efficiency of the
semi-Lagrangian method for the incompressible flow,
Inter. J Numer. Meth. Fluids, 2001, 35, p319-340.
- W.Borchers, S.Krautle, R.Pasquetti, R.Rautmann,
K.Wielage, C.J.Xu, Towards a parallel hybrid highly accurate
Navier-Stokes solver, Numerical Flow Simulation II, NNFM 75,
Hirschel Ed., Springer, 2001.
- C.J. Xu, An efficient method for the Navier-Stokes/Euler
coupled equations via a spectral element approximation,
SIAM J. Numer. Anal., 2000, 38(4), p1217-1242.
- C.J. Xu, Y.M. Lin, Open boundary conditions for the spectral
simulation of Poiseuille-Benard flow, Acta mechanica sinica, 2000,
32(1), p1-10.
- C.J.Xu, Y.M. Lin, Analysis of iterative methods
for the viscous/inviscid
coupled problem via a spectral element approximation,
Inter. J Numer. Meth. Fluids, 2000, 32, p619-646.
- C.J.Xu, An iterative method for the
Navier-Stokes/Euler coupled equations, J. Comput. Math., 1999, 4,
p379-396.
- C.J.Xu, W.Z.Shen, A spectral element method for Helmholtz equations
with singularities, In Proceeding of international conference on
numerical PDE(Congqing), World Scientific, Singapore, 1998.
- C.J.Xu, Y.Maday, A Spectral element method for the Euler equations:
Application to flow simulations,
J. Computational and Applied Mathematics, 1998, 91(1), p63-85.
- C.J.Xu, Y.Maday, A global algorithm in spectral method
for viscous/inviscid coupling,
Chinese Annual of Math.(B), 1997, 18(2), p191-200.
- C.J.Xu, A spectral element method for Helmholtz type equations with
singularities, J.of Xiamen Univ., 1997, 36(2), p176-183.
- C.J.Xu, A global algorithm on the coupling of
Navier-Stokes/Euler equations, Houston J. of Mathematics, 1996,
ICOSAHOM'95, p151.
- C.J.Xu, A slight over-integration method for 2-D
Euler equations, Chinese Annual of Math.(A), 1996, 17(5),
p519-524.
- C.J.Xu, A slight overintegration spectral method approximation
on the 2D evolutional Euler equations,
Chin.J.of Contemporary Math., 1996, 17(4), p319-327.
- C.J.Xu, L.K.Gu, Notes on the spectral methods for fluid
dynamics, J.of Math.Study, 1995, 28(4), p1-8.
- C.J.Xu, Y.Maday, On coupling of the Navier-Stokes and
Euler equations: Resolution by a spectral method, In Proceeding of
Scientific and Engineering Computing,
National defence industry press, 1994, p246-249.