工作经历：

研究方向：

论文：

- 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;

- Hui Yao, Mejdi Azaiez, and Chuanju Xu, New Unconditionally Stable Schemes for the Navier-Stokes Equations , Communications in Computational Physics, 2021, 30,p1083-1117;

- 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;

- Enze Shi and Chuanju Xu, A comparative investigation of neural networks in solving differential equations , Journal of Algorithms & Computational Technology, 2021, 15,1748302621998605;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- Chuanju Xu, Spectral methods for some kinds of fractional differential equations , Handbook of Fractional Calculus with Applications, De Gruyter, 2019, 3, p101-126;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- Xiaojun Zhou and Chuanju Xu, Analysis of a system of autonomous fractional differential equations, International Journal of Biomathematics, 2017, 10(07), 1750094;

- 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;

- 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;

- 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;

- 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;

- 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;

- Dianming Hou and Chuanju Xu, A fractional spectral method with applications to some singular problems, Advances in Computational Mathematics, 2017, 43(5), p911-944;

- 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;

- 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;

- Shimin Lin and Chuanju Xu, Theoretical and Numerical Investigation of Fractional Differential Equations (in Chinese), Mathematica Numerica Sinica, 2016, 38(1), p1-24;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- Xingyang Ye and Chuanju Xu, A posteriori error estimates for the fractional optimal control problems, Journal of Inequalities and Applications, 2015, 141, p1-13;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- Xingyang Ye, Chuanju Xu, Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem, Numer. Math. Theor. Meth. Appl., 2013, 6(3), p499-519;

- Dong Qu, Chuanju Xu, Generalized Polynomial Chaos Decomposition and Spectral Methods for the Stochastic Stokes Equations, Computers & Fluids, 2013, 71, p250-260;

- 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;

- Yumin Lin, Xianjuan Li, and Chuanju Xu, Finite Difference/ Spectral Approximation for the Fractional Cable Equations, Mathematics of Computation, 2011, 80(275), p1369-1396;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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;

- 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 Channe , 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.