Prof. Dr. Xinyuan Wu

Welcome to the Homepage of Xinyuan Wu

 

Professor in Department of Mathematics, Nanjing University

• Board Member of China Society for Computational Mathematics
• Reviewer of Mathematical Reviews
• Memberships in professional societies
  • SIAM (Society for Industrial and Applied Mathematics )
  • AMS (American Mathematical Society)

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Research Interests

• Geometric Algorithms for Differential Equations

• Numerical Methods for Stiff Problems

• Numerical Methods for Algebraic Systems

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Foundations

• Taking Charge of Grant 11671200 from National Natural Science Foundation of China
• Taking Charge of Grant 20130091110041 from Research Foundation for the Doctoral Program of Higher Education
• Taking Charge of Grant 10771099 from National Natural Science Foundation of China
• Taking Charge of Grant 20100091110033 from Research Foundation for the Doctoral Program of Higher Education
• Taking Charge of Grant 9112020301 from Institute of Key Basic Research Project
• Taking Charge of Grant 11271186 from National Natural Science Foundation of China
• Taking Charge of Grant 11311112 from National Natural Science Foundation of China

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• Organized 2011 Nanjing Symposium on Structure-Preserving Algorithms for Differential Equations （Aug.15 - Aug.17, 2011）(Chair of the Organizing Committee)

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2011 Nanjing Symposium on Structure-Preserving Algorithms for Differential Equations （Aug.15 - Aug.17, 2011）

• Organized 2nd International Conference on Numerical Analysis of Differential Equations, Nanjing, 2012 （ICNADE2012, Jun. 15-Jun.17, 2012, Nanjing）(Chair of the Organizing Committee)

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2nd International Conference on Numerical Analysis of Differential Equations (Jun.15-Jun.17,2012)

• Organized 3rd International Conference on Numerical Analysis of Differential Equations, Nanjing, 2013 （ICNADE2013, Mar. 29-Mar.31, 2013, Nanjing）(Chair of the Organizing Committee)

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3rd International Conference on Numerical Analysis of Differential Equations (Mar.29-Mar.31,2013)

• Organized 4th International Conference on Numerical Analysis of Differential Equations, Nanjing, 2014 （ICNADE2014, May. 08-May.10,  2014, Nanjing）(Chair of the Organizing Committee)

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4th International Conference on Numerical Analysis of Differential Equations (May.08-May.10,2014)

• Organized 2014 Nanjing Workshop on Structure-Preserving Algorithms for Differential Equations, （Nov. 28-Nov. 30  2014, Nanjing） (Chair of the Organizing Committee)

　

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2014 Nanjing Workshop on Structure-Preserving Algorithms for Differential Equations (Nov.28-Nov.30,2014)

• Organized Mini Workshop on Numerical Analysis of ODEs, （Jointly organized by Nanjing University and University of Auckland, Apr. 14-Apr. 15, 2015, Nanjing）

　

For the detail,  please kindly click the following link:

Mini Workshop on Numerical Analysis of ODEs (Apr.14-Apr.15,2014)

　

• Organized 2015 Nanjing Symposium on Workshop on Structure-Preserving Algorithms for Differential Equations, （Jointly organized by Nanjing University and University of Cambridge , Aug. 2-Aug. 4, 2015, Nanjing）

　

For the detail,  please kindly click the following link:

2015 Nanjing Symposium on Structure-Preserving Algorithms for Differential Equations (Aug.2-Aug.4,2015)

　

• Organized 2016 Nanjing Workshop on Structure-Preserving Algorithms for Differential Equations, （Jointly organized by Nanjing University and University of Cambridge , Aug. 8-Aug. 10, 2016, Nanjing）

For the detail,  please kindly click the following link:

2016 Nanjing Workshop on Structure-Preserving Algorithms for Differential Equations (Aug.8-Aug.10,2016)

 

• Organized 2017 Qufu Workshop on Structure-Preserving Algorithms for Differential Equations, （Jointly organized by Qufu normal University and Nanjing University, Jun. 9-Jun. 11, 2017, Qufu）

 

• Organized 2018 Zaozhuang Workshop on Structure-Preserving Algorithms for Differential Equations, （Jointly organized by Zaozhuang University and Nanjing University, Mar. 31-Apr. 2, 2018, Zaozhuang）

 

•  Organized 2018 Hebei Normal University Workshop on Numerical Analysis for Differential Equations, （Jointly organized by Hebei Normal University and Nanjing University, December 7-8, 2018, Shijiazhuang）　

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Monographs

• The monograph, entitled “Geometric Integrators for Differential Equations with Highly Oscillatory Solutions”, (ISBN 978-7-03-067112-7) was jointly published by Science Press and Springer Nature Singapore Ptd. 2020. It is noted that Springer Nature edition (ISBN 978-981-16-01460-0) will be published in 2021.

For the detail, please kindly click the following link:

https://www.springer.com/gp/book/9789811601460

 

• The monograph, entitled “Structure-Preserving Algorithms for Oscillatory Differential Equations”, (ISBN 978-3-642-35338-3) was published by Springer Press.

For the detail, please kindly click the following link:

Structure-Preserving Algorithms for Oscillatory Differential Equations

The reviews of this monograph have been presented by 《Matehmatical Reviews》 and 《Zentralblatt MATH》. For details, please kindly click the following link:

     American Mathematical Society (AMS)        Zentralblatt MATH (zbMATH)

　

• The monograph, entitled “Structure-Preserving Algorithms for Oscillatory Differential Equations II”，(ISBN 978-3-662-48155-4) was published by Springer Press.
  

For the detail, please kindly click the following link:

Structure-Preserving Algorithms for Oscillatory Differential Equations II

The reviews of this monograph have been presented by 《Matehmatical Reviews》 and 《Zentralblatt MATH》. For details, please kindly click the following link:

     American Mathematical Society (AMS)        Zentralblatt MATH (zbMATH)  

 

• The monograph, entitled “Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations” published by Springer Press ISBN: 978-981-10-9003-5 and 978-981-10-9004-2(eBook) (jointly published with Science Press, Bejing, China, ISBN: 978-7-03-055128-3).       

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Contributions to International Conferences  　

• 26 April 2021, delivered invited talk: “Geometric Integrators for Differential Equations with Highly Oscillatory Solutions”in the Webinar on Materials Science, Engineering and Technology held during 23 -26 April 2021. Honored with VEBLEO SCIENTIST AWARD, during this conference, from VEBLEO.

• Sep. 08-14, 2019, invited talk:“Symplectic Approximations for Klein--Gordon Equations”, 2019 Conference on Geometric Numerical Integration of Differential Equations, AMSS, Chinese Academy of Sciences, China.

• Feb. 19-23, 2018, invited talk: ``ERKN integrators for multi-frequency highly oscillatory differential equations", ANODE 2018, Auckland.

• Sep. 25-30, 2017， Highlighted invited Speaker (One hour talk) in ICNAAM 2017,15th International Conference of Numerical Analysis and Applied Mathematics: "ERKN Integrators Solving Multi-Frequency Highly Oscillatory Systems with Applications"，Thessaloniki, Greece. Awarded the highest distinction of “Honorary Fellowship” 2017, during this conference, from European Society of Computational Methods in Sciences, and Engineering.

• Aug. 31-Sep. 1, 2017， invited talk: ``ERKN Integrators Solving Nonlinear Klein—Gordon equations", Conference From Computation to Information: Recent Advances in Numerical Analysis, at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge.

• May 30-Jun. 3 2017， invited talk: “ERKN Integrators Solving Nonlinear Wave Equations”， Third International Conference on Engineering and Computational Mathematics (ECM2017), Hong Kong.

• Dec.10-14, 2016, ivited talk: "Variation-of-constants formula with applications to structure-preserving computation", 20th IMACS World Congress, Xiamen University, China.

• Nov. 13-16, 2015, invited talk: "Operator-Variation-of-Constants Formula with Applications", Workshop on SDEs, Shanghai Normal University, China.

• Dec. 7-13, 2014, invited talk: "Semi-analytical explicit integrators for solving wave equations", The 5th International Conference on Scientific Computing and Partial Differential Equations, Baptist University, Hong Kong.

• Sep. 02-05, 2013, invited talk: "Structure-Preserving Algorithms for Multi-Frequency Oscillators", 
  LMS Minisymposium,Advanced Decomposition Methods for Partial Differential Equations, Kingston University，UK.    

• Jul.14-19, 2013, invited talk: "Structure-Preserving Algorithms for Multi-frequency Oscillatory  
  Differential Equations", ICCM 2013, National Taiwan University, Taiwan.

• Jan. 7-11, 2013,invited talk: "Structure-Preserving Algorithms for Oscillatory Differential Equations", ANODE 2013 Conference-Auckland Numerical Ordinary Differential Equations, New Zealand.

• Sep. 16-17, 2011, invited talk: "Structure-preserving ERKN Integrators", Baylor Workshop on Splitting and Multiscale Methods for Computational PDEs, Waco,Texas,USA.               

• Jul. 18-22, 2011, invited talk: "A novel approach to solving nonlinear oscillatory systems",7th International Congress on Industrial & Applied Mathematics，Vancouver, Canada.

• Jun. 27-30, 2010, invited talk: "ESRKN methods for Hamiltonian Systems", Computational and Mathematical Methods in Science and Engineering, Almeria, Spain.

• Sep. 18-22, 2009, invited talk: "On Multidimensional ARKN methods for Systems of Perturbed Oscillators", International Conference on Numerical Analysis and Applied Mathematics,Rethymno Greece.

• May 27-29, 2009, invited talk: "A New Improved Iteration Refinement with Roundoff Error Analysis", International Conference on Engineering and Computational Mathematics 2009, Hong Kong.

• Sep. 16-20, 2008, invited talk: "RKN Methods Based on Exact Flows of Both Internal Stages and Update for Solving Perturbed Oscillators", International Conference on Numerical Analysis and Applied Mathematics, Psalidi, GREECE. 

• Nov. 07-11, 2005, invited talk: "On extended Runge-Kutta-like methods for ODEs", 6th Frontier Science Symposium, National University of Singapore, Singapore.

• Oct. 29-Nov 1, 1997, invited talk: "A dynamic method for weighted linear least squares problems", Sixth  SIAM Conference on Applied Linear Algebra, Utah, USA.

• Oct. 17-20, 1995, invited talk: "Applications of ODE methods", 2nd Asian Mathematical Conference, Suranaree Univ Technol, Nakhon Ratchasima, Thailand.

• Oct. 26-30, 1992, invited talk: "The Method of Ordinary Differential Equation for Solving Linear Algebraic Equations", 92' Shanghai International Conference on Numerical Algebra with Applications, Shanghai, China.

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Recent professional activities

• May 13-14, 2021, China Univ. Petro., China (invited by Prof. Dr. Weiguo Li)

• May 12-13, 2021, Shandong University, China (invited by Prof. Dr. Weidong Zhao)

• May 10-11, 2021, Chinese Academy of Sciences, China (invited by Prof. Dr. Jialin Hong)

• July 2-31 , 2019, University of Cambridge (invited by Prof. A. Iserles)

• Jan. 30.- Feb. 28, 2019, The University of Sydney (invited by Prof. Q. Wang)

• Aug. 20-Sep. 18, 2018 , Universitat Tubingen, Germany (invited by Prof. Dr. Christian Lubich).

• May 28- Jun 7, 2018, The University of Firenze (invited by Prof. L. Brugnano).

• May 14- May 27, 2018, The University of Bath (invited by Dr. A. Hill).

• Feb. 15- Mar. 15, 2018, The University of Auckland (invited by Prof. J. Butcher and Dr S. Wang).

• Aug. 30- Sep. 8, 2017, The University of Cambridge (invited by Dr. Carola-Bibiane Schönlieb).

• Aug. 9-30, 2017, Universitat Tubingen, Germany (invited by Prof. Dr. Christian Lubich).

• Jul. 30-Aug. 5, 2017, The University of Bath (invited by Dr. Hill T. Adrian).

• Jul.. 8-29，2017 ，The University of Cambridge （invited by Prof. Arieh Iserles）.

• Jan. 4-31, 2017, The University of Aucklan （invited by Prof. John Butcher and Prof. Bernd Krauskopf）.

• Feb. 1-16, 2017, The University of Sydney (invited by Prof. Qiying Wang)

• Feb. 17-25, 2017, Australian Nantinoanl University (invited by Prof. Markus Hegland and Prof. Pier Bouwknegt)

• Sep. 01-21, 2016, University of Nevada Las Vegas, USA (invited by Prof. Dr. Jichun Li).

• Jul. 01-29, 2016, University of Cambridge, UK (invited by Prof. Dr. Arieh Iserles).

• Feb. 15-18, 2016, Massey University, New Zealand (invited by Prof. Robert Mclachlan).

• Jan. 28-Feb 14, 2016, The University of Auckland, New Zealand (invited by Prof. John Butcher).

• Jan. 18-28, 2016, La Trobe University, Australia (invited by Prof. Dr. Reinout Quispel).

• Aug. 12-25, 2015, KIT, Germany (invited by Prof. Dr. Tobias Jahnke).

• Jul. 01-28, 2015, University of Cambridge, UK (invited by Prof. Dr. Arieh Iserles).

• Sep. 17-25, 2014, Universitat Tubingen, Germany (invited by Prof. Dr. Christian Lubich).

• Sep. 12-16, 2014, KIT, Germany (invited by Prof. Dr.Tobias Jahnke).

• Jul. 21-Aug. 15, 2014, University of Cambridge, UK (invited by Prof.Dr. Arieh Iserles).

• Sep. 06-13, 2013, University of Greenwich, UK (invited  by Prof. Dr. C. H. Lai )

• Aug. 08-10, 2013, Chinese Academy of Sciences, China (invited  by Prof. Dr. Yifa Tang)

• Jan. 03-20, 2013, The University of Auckland, New Zealand (invited by Prof. John Butcher and Dr. Robert. Chan).

• Sep. 17-23, 2012, University of Bath, UK (invited by Prof. I.G.Graham and Dr. Adrian Hill).   

• Sep. 05-17, 2012, University of Cambridge, UK (invited by Prof.Dr. Arieh Iserles).

• Nov. 23-Dec 06, 2011, Universitat Tubingen, Germany (invited by Prof. Dr. Christian Lubich).

• Nov. 30-Dec 02, 2011, Heinrich-Heine-University, Germany (invited by Prof. Dr. Achim Schädle).

• Sep. 19-24, 2011, Purdue University West Lafayette, IN, USA (invited by Dr. Jianlin Xia).

• Sep. 14-19, 2011, Baylor University, Waco, Texas, USA (invited by Prof. Dr. Tim Sheng).

• Jul. 23-30，2011, McGill University, Montreal, Canada (invited by Prof. Dr. Xiaowen Chang).

• Dec. 11-19, 2010, The University of Auckland, Auckland, New Zealand (invited by Prof. J.C. Butcher).

• Dec. 06-10, 2010, La, Trobe University (invited by Prof. Reinout Quispel & Dr. David Mclaren).

• Sep. 10-14, 2010, Chinese Academy of Sciences, China (invited  by Prof. Dr. Jialin Hong).

• Sep. 02-08, 2010, Imperial College London (invited by Prof. Jeff Cash).

• Jul. 27-Aug 10, 2010, CMMSE 2010, Universidad de Salamanca (invited by Prof. Dr. Jesus Vigo-Aguiar).

• Sep. 18-22, 2009, ICNAAM 2009, Organizer of a sessionworkshop in ICNAAM 2009, 7th International Conference Numerical Analysis and Applied Mathematics, Greece (invited by Prof. Dr.Theodore E. Simos).

• Oct. 01-08, 2008, Universitat Tubingen, Germany (invited by Prof. Dr. Christian Lubich).

• Sep. 21-25, 2008, Institut fur Angewandte und Numerische Mathematik, Germany (invited by Prof. Dr.Tobias Jahnke).

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Recent Publications

• A unified framework for the study of high-order energy-preserving integrators for solving Poisson systems. J. Comput. Phys., 2021 in press (joint work with L. Mei and L. Huang)

• Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems. SIAM J. Sci. Comput., 2021 in press (joint work with L. Mei and L. Huang)

• Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral. Appl. Math. Comput. 397 (2021), 125980, 8 pp. (joint work with F.Z. Geng)

• Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs. Numer. Algorithms 86 (2021), no. 2, 693–727 (joint work with B. Wang and L. Mei)

• Continuous trigonometric collocation polynomial approximations with geometric and superconvergence analysis for efficiently solving semi-linear highly oscillatory hyperbolic systems. Calcolo 58 (2021), no. 1, Paper No. 6, 34 pp. (joint work with C. Liu)

• Energy-preserving exponential integrators of arbitrarily high order for conservative or dissipative systems with highly oscillatory solutions. J. Comput. Phys. 442 (2021) 110429 (joint work with L. Mei and L. Huang)

• Kernel functions-based approach for distributed order diffusion equations. Numer. Methods Partial Differential Equations 37 (2021), 1269–1281 (joint work with F.Z. Geng)

• A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems. 2021 BIT Numerical Mathematics (joint work with B. Wang)

• A novel class of explicit divergence-free time-domain methods for efficiently solving Maxwell's equations. Comput. Phys. Commun., 2021 in press (joint work with H. Yang and X. Zeng)

• Efficient implementation of the ARKN and ERKN integrators for multi-frequency oscillatory systems with multiple time scales. Appl. Numer. Math. 151 (2020), 13–26 (joint work with W. Shi and K. Liu)

• Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations. Appl. Numer. Math. 153 (2020) 352–380 (joint work with C. Liu)

• A two-step symmetric method for charged-particle dynamics in a normal or strong magnetic field. Calcolo 57 (2020), no. 3, Paper No. 29, 21 pp. (joint work with B. Wang and Y. Fang)

• Exponential collocation methods based on continuous finite element approximations for efficiently solving the cubic Schr?dinger equation. Numer. Methods Partial Differential Equations 36 (2020), no. 6, 1735–1757 (joint work with B. Wang)

• A continuous-stage modified leap-frog scheme for high-dimensional semi-linear Hamiltonian wave equations. Numer. Math. Theor. Meth. Appl.13 (2020) 814-844 (joint work with B. Wang and Y. Fang)

• Geometric Integrators for Differential Equations with Highly Oscillatory Solutions. Science Press and Springer Nature Singapore Ptd. 2020 (joint work with B. Wang)

• Volume-preserving exponential integrators and their applications. J. Comput. Phys. 396 (2019) 867–887 (joint work with B. Wang)

• Long-time momentum and actions behaviour of energy-preserving methods for semilinear wave equations via spatial spectral semi-discretizations, Adv. Comput. Math., doi.org/10.1007/s10444-019-09719-4. In Press, 2019 (joint work with B. Wang)

• Energy-preserving continuous stage extended Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems, Appli. Numer. Math. 145 (2019) 469–487 (joint with J. Li)

• Semi-analytical exponential RKN integrators for efficiently solving high-dimensional nonlinear wave equations based on FFT techniques, Comput. Phys. Comm.  243 (2019) 68-80 (joint work with L. Mei et al.)

• Explicit Gautschi-type integrators for nonlinear multi-frequency oscillatory second-order initial value problems, Numer. Algo. 81 (2019) 1275-1294 (joint with W. Shi)

• Global error bounds of one-stage extended RKN integrators for semilinear wave equations, Numer. Algo. 81 (2019) 1203-1218 (joint with B. Wang)

• Numerical Analysis of an energy-preservation scheme for two-dimensional Hamiltonian wave equations with Numann boundary conditions, Int. J. Numer. Anal. Model. 16 (2019) 319-339 (joint with C. Liu and W. Shi)

• Exponential collocation methods for conservative or dissipative systems, J. Comput. Appl. Math. 360 (2019) 99-116 (joint with B. Wang)

• A symplectic approximation with nonlinear stability and convergence analysis for efficiently solving semi-linear Klein–Gordon equations, Appli. Numer. Math. 142 (2019) 64-89 (joint with B. Wang)

• The existence of explicit symplectic ARKN methods with several stages and algebraic order greater than two, J. Comput. Appl. Math. 353 (2019) 204-209 (joint with J. Li and W. Shi)

• ERKN integrators solving multi-frequency highly oscillatory systems with applications, AIP Conference Proceedings 1978, 020005 (2018) (joint with B. Wang)

• New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions, Appli. Math. Comput. 339 (2018) 588-606 (joint with C. Liu and W. Shi)

• The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear "Klein-Gordon equations", IMA J. Numer. Anal. 39 (2019) 2016-2044 (joint with Bin Wang)

• Functionally-fitted energy-preserving integrators for Poisson systems, J. Comput. Phys., 364 (2018) 137-152（joint with Bin Wang）

• Symmetric and arbitrarily high-order Birkhoff–Hermite time integrators and their long-time behaviour for solving nonlinear Klein–Gordon equations，J. Comput. Phys., 356 (2018) 1-30 (joint with Changying Liu and A. Iserles)

• Extended phase properties and stability analysis of RKN-type integrators for solving general oscillatory second-order initial value problems, Numer. Algo., 77 (2017) 37-56 (joint with K. Liu and W. Shi)

• A linearly-fitted conservative (dissipative) scheme for efficiently solving conservative (dissipative) nonlinear wave PDEs,J Comput. Math., 35 (2017) 780-800 (joint with K. Liu and W. Shi)

• Exponential fourier collocation methods for solving first-order differential equations,J Comput. Math., 35 (2017) 711-736 (with B. Wang, F. Meng and Y. Fang)

• The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications. Appl. Math. Lett., 74 (2017) 60-67 (joint with Changying Liu)

• Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations. J. Comput. Appl. Math. 313 (2017). 185-201 (joint with Bin Wang et al.)

• Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations，J. Comput. Phys., 340 (2017) 243-275 (joint with Changying Liu)

• Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems, J. Comput. Phys., 338 (2017) 567-584 (joint with Lijie Mei)

• An essential extension of the finite-energy condition for extended Runge--Kutta--Nystr\"{o}m integrators  when applied to nonlinear wave equations，Commun. Comput. Phys., 22 (2017) 742-764 (joint with Lijie Mei et al.)

• An improved tri-colored rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems, Numer. Algo., 75 (2017) 909-935 (joint with Hongli Yang et al.)

• The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications, J. Comput. Phys., 323(2016) 171–190 (joint with Lijie Mei)

• Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems, SIAM J. SCI. Comput., 38(2016） A1876-A1895 (joint with Yu-Wen Li)

• Functionally-fitted energy-preserving methods for solving oscillatory nonlinear Hamiltonian systems, SIAM J. Numer. Anal., 54(2016) 2036-2059 (joint with Yu-Wen Li)

• An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations, J. Math. Anal. Appl., 440(2016) 167-182 (joint with Changying Liu)

• A new framework for solving partial differential equations using semi-analytical explicit RK(N)-type integrators, J. Comput. Appl. Math., 301(2016), 74-90  (joint with Changying Liu and Lijie Mei)

• An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations with its applications, J. Math. Phys., 57(2016), 021504 (joint with Changying Liu)

• General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs, J. Comput. Phys., 301(2015), 141-166 (joint with Yu-Wen Li)

• An analytical expression of solutions to nonlinear wave equations in higher dimensions with Robin boundary conditions, J. Math. Anal. Appl., 426(2015), 1164-1173 (joint with Lijie Mei and Changying Liu)

• High-order symplectic and symmetric composition methods for multi-frequency and multi-dimensional oscillatory Hamiltonian systems, J. Comput. Math., 33(2015), 355–377 (joint with Kai Liu)

• Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems, Found. Comput. Math., 16(2016), 151-181 (joint with Bin Wang and A. Iserles）

• An efficient  high-order explicit  scheme for  solving  Hamiltonian nonlinear wave equations, Appl Math Comput.，246(2014), 696-710 （joint with Changying Liu and Wei Shi）

• Improved Filon-type asymptotic methods for highly oscillatory differential equations with multiple time scales, J. Comput. Phys., 276(2014), 62-73 (joint with Bin Wang)

• A simplified Nystrom-tree theory for extended Runge-Kutta-Nystrom integrators solving multi-frequency oscillatory systems, Comput. Phys. Comm., 185(2014), 2841-2850 (joint with Hongli Yang et al.)

• Explicit multi-frequency symmetric extended RKN integrators for solving multi-frequency and multidimensional oscillatory reversible systems, CALCOLO, 52(2015), 207-231 (joint with Bin Wang)

• Multidimensional ARKN methods for general oscillatory second-order initial value problems,
   Comput. Phys. Comm., 185(2014), 1999–2007 (joint with Kai Liu)

• A highly accurate explicit symplectic ERKN method for multi-frequency and multidimensional oscillatory Hamiltonian systems. Numer. Algo., 65(2014), 705-721 (joint with Bin Wang)

• Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations, Appl. Numer. Math.,74(2013), 17-34(joint with Bin Wang and Jianlin Xia)

• Error analysis of explicit TSERKN methods for highly oscillatory systems, Numer. Algo., 65(2014), 465-483 (joint with Jiyong Li)

• A note on symplectic and symmetric ARKN methods, Comput. Phys. Comm., 184(2013), 2408-2411(joint with Wei Shi)

• Order conditions for RKN methods solving general second-order oscillatory systems, Numer. Algo., 66(2014), 147-176 (joint with Xiong You, Jinxi Zhao, HongliYang and Yonglei Fang)

• An extended discrete gradient formula for oscillatory Hamiltonian systems, J. Phys. A: Math. Theor. 46 (2013) 165203(joint with Kai Liu and Wei Shi)

• A Filon-type asymptotic approach to solving highly oscillatory second-order initial value problems, J. Comput. Phys. 243(2013), 210-223(joint with Bin Wang and Kai Liu)

• Effective integrators for nonlinear second-order oscillatory systems with a time-dependent frequency matrix,  Appl. Math. Modell. 37(2013), 6505-6518 (joint with Bin Wang and Wei Shi)

• Efficient energy-preserving integrators for oscillatory Hamiltonian systems,  J. Comput. Phys., 235(2013) 587-605 (joint with Bin Wang and Wei Shi)

• Novel improved multidimensional Stormer-Verlet formulas  with applications to four aspects in scientific computation, Math. Comput. Model., 57(2013) 857-872. (joint with Bin Wang and Hua Zhao)

• Explicit Multi-Symplectic Extended Leap-frog Methods for Hamiltonian Wave Equations, J. Comput. Phys.,231(2012) 7671-7694.(joint with Wei Shi and Jianlin Xia)

• Adapted Falkner-type methods solving oscillatory second-order differential equations，Numer. Algo.,62(2013) 355-381 (joint with Jiyong Li)

• Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nystrom methods,  BIT Numer. Math., 52(2012) 773-795.(joint with Bin Wang and Jianlin Xia)

• ERKN methods for long-term integration of multidimensional orbital problems,  Appl. Math. Modell., 37(2013) 2327-2336.(joint with  Bin Wang et al.)

• A new high precision energy-preserving integrator for system of oscillatory second-order differential equations, Phys. Lett. A., 376 (2012) 1185-1190. (joint with Bin Wang)

• On symplectic and symmetric ARKN methods, Comput. Phys. Comm., 183(2012) 1250-1258. (joint with Wei Shi)

• A note on stability of multidimensional adapted Runge-Kutta-Nystrom methods for oscillatory systems，Appl. Math. Modell., 36 (2012) 6331–6337.

• On extended RKN integrators for multidimensional perturbed oscillators with applications, Appl. Math. Modell,36(2012) 1504-1513. (joint with B. Wang et al.)

• Two-step extended RKN methods for oscillatory systems, Comput. Phys. Comm.,182 (2011) 2486-2507. (joint with J. Li et al.)

• A note on Wilkinson's iterative refinement of solution with automatic step-size control,Inter. J. Comput. Math., 88 (2011), 1192-1200. (joint with X. Wu)

• A new iterative refinement with roundoff error analysis, Numer. Linear Algebra Appl., 18 (2011), 275-282.(joint with Z. Wang)

• Multidimensional adapted Runge-Kutta-Nystrom  methods for oscillatory systems, Comput. Phys. Comm., 181 (2010), 1955-1962. (joint with B. Wang)

• Extended RKN methods with FSAL property for oscillatory systems, Comput. Phys. Comm., 181 (2010), 1538-1548. (joint with Y. Fang et al.)

• ERKN integrators for systems of oscillatory second-order differential equations, Comput. Phys. Comm., 181 (2010), 1873-1887. (joint with X. You et al.)

• Extended RKN-type methods with minimal dispersion error for perturbed oscillators, Comput. Phys. Comm., 181 (2010),  639-650. (joint with Y. Fang et al.)

• Comments on "embedded pair of extended Runge-Kutta-Nystrom type methods for perturbed oscillators", Appl. Math. Modell., 34 (2010)，3708-3711. (joint with B. Wang)

• Order conditions for ARKN methods solving oscillatory systems, Comput. Phys. Comm., 180 (2009)，2250-2257. (joint with X. You et al.)

• Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Comm., 180 (2009)，1777-1794. (joint with H. Yang et al.)

• A semi-local convergence theorem for a robust revised Newton's method, Comput. Math. Appl., 58 (2009), 1320-1327. (joint with Z. Wang)

• On energy conservation and P-stability, Appl. Math. Modell., 33 (2009), 4146-4152. (joint with Q. Li et al.)

• Iterative refinement of computing inverse matrix, Inter. J. Comput. Math., 86 (2009), 1126-1134. (joint with J. Wu)

• Note on derivation of order conditions for ARKN methods for perturbed oscillators, Comput. Phys. Comm., 180 (2009), 1545-1549. (joint with X. You et al.)

• A robust trigonometrically fitted embedded pair for perturbed oscillators, J. Comput. Appl. Math., 225 (2008), 347-355. (joint with Y. Fang et al.)

• New embedded pairs of explicit Runge-Kutta methods with FSAL properties adapted to the numerical integration of oscillatory problems, Phys. Lett. A, 372 (2008), 6551-6559. (joint with Y. Fang et al.)

• Trigonometrically fitted explicit Numerov-type method for periodic IVPs with two frequencies, Comput. Phys. Comm., 179 (2008), 801-811.(joint with Y. Fang et al.)

• Trigonometrically-fitted ARKN methods for perturbed oscillators, Appl. Numer. Math., 58 (2008), 1375-1395. (joint with H. Yang)

• A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions, Appl. Numer. Math., 58 (2008), 341-351. (joint with Y. Fang)

• A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators, Appl. Numer. Math., 57 (2007), 166-175. (joint with Y. Fang)

• Order conditions for integrators and mappings with applications, Nonlinear Analysis, 67 (2007), 2589-2608.

• A two-step explicit P-stable method of high phase-lag order for linear periodic IVPs, J. Comput. Appl. Math., 200 (2007), 287-296. (joint with Q. Li)

• Study of general Taylor-like explicit methods in solving stiff ordinary differential equations, Inter. J. Comput. Math., 84 (2007), 1795-1803. (joint with J. Xia)

　

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Teaching

• Calculus

• Linear Algebra

• Differential Equations

• Numerical Analysis

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My Ph.D and Postdoctoral Students

• Yonglei Fang, Ph.D, graduated from my university, 2007, title of his dissertation: Numerical methods for periodical initial value problems.

• Hongli Yang, Ph.D, graduated from my university, 2009, title of her dissertation: Long-time Integration of Oscillatory Hamiltonian Problems.

• Xiong You, Ph.D, graduated from my university, 2009, title of his dissertation: Structure-Preserving Methods for Systems of Differential-Algebraic Equations and Systems of Oscillatory Differential Equations.

• Qinghong Li, Postdoctoral, finished the research program in my university, 2009, title of his dissertation: Structure-preserving methods for periodic initial value problems.

• Jiyong Li, Ph.D, graduated from my university, 2012, title of his dissertation: The Study of Numerical Methods for Second-order Oscillatory Differential Equations.

• Bin Wang,  Ph.D., graduated from my university, 2013,  Joint Ph.D. student at University of Cambridge   (2011.09-2012.09), title of his dissertation: Geometric Integrators for Multi-frequency Oscillatory Differential Equations.

• Wei Shi,  Ph.D., graduated from my university, 2014,  Joint Ph.D. student at Purdue University   (2012.09-2013.09), title of her dissertation: Structure-preserving Methods for Oscillatory Hamiltonian systems.

• Kai Liu, Ph.D., graduated from my university, 2015. Joint Ph.D. student at University of Cambridge  (2014.01-2015.01)

• Lijie Mei, Ph.D., graduated from my university, 2016.

• Yuwen Li, Master, graduated from my university, 2016.

• Changying Liu, Ph.D., graduated from my university, 2017. Joint Ph.D. student at University of Cambridge (2015.03-2015.09), title of his dissertation: Structure-preserving Algorithms for Nonlinear PDEs.

• Xianyang Zeng, current Ph.D.student. Start date September 2015.

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Contact

• E-Mail:   xywu@nju.edu.cn

• Address:  Department of Mathematics, Nanjing University, Nanjing 210093, China

• Office:   Building for Department of Mathematics, Room 209-3

• Phone:    86 25 83686665

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last updated in 09/07/2021