Edit Profile (opens in new tab) Wu, Xinyuan Compute Distance To: Compute Author ID: wu.xinyuan Published as: Wu, Xinyuan; Wu, Xin-Yuan; Wu, Xin-yuan; Wu, X. Y.; Wu, X.-Y. more...less Homepage: http://maths.nju.edu.cn/~XYWUMATHNJU/ External Links: ResearchGate · dblp Documents Indexed: 173 Publications since 1985, including 4 Books Co-Authors: 41 Co-Authors with 141 Joint Publications 1,836 Co-Co-Authors all top 5 Co-Authors 30 single-authored 35 Wang, Bin 19 Shi, Wei 18 Xia, Jianlin 15 Fang, Yonglei 14 Liu, Changying 12 You, Xiong 10 Liu, Kai 9 Li, Qinghong 9 Mei, Lijie 7 Yang, Hongli 5 Li, Jiyong 5 Ouyang, Zixiang 3 Huang, Li 3 Li, Yuwen 3 Luo, Liangsheng 3 Shao, Rong 3 Song, Yongzhong 3 Wang, Zhengyu 3 Wu, Zhonglin 3 Zeng, Xianyang 3 Zhao, Hua 2 Geng, Fazhan 2 Iserles, Arieh 2 Meng, Fanwei 2 Wu, Hongwei 2 Yang, Fan 2 Zhao, Dawei 2 Zhu, Yiran 1 Chen, Zhaoxia 1 Fu, Dongsheng 1 Liu, Yuhan 1 Ming, Qinghe 1 Ning, Xinbao 1 Ralescu, Dan A. 1 Ru, Zhengliang 1 Shen, Zuhe 1 Wang, Lei 1 Wu, Hohgwei 1 Wu, Jun 1 Wu, Xiaoxuan 1 Xu, Hongyi 1 Xue, Guohe 1 Zhao, Jinxi all top 5 Serials 29 Applied Mathematics and Computation 13 Computer Physics Communications 13 Journal of Computational Physics 10 Journal of Nanjing University. Mathematical Biquarterly 10 Applied Numerical Mathematics 9 Numerical Algorithms 8 Computers & Mathematics with Applications 7 Journal of Computational and Applied Mathematics 6 Numerical Mathematics 6 Applied Mathematical Modelling 4 Calcolo 4 Journal of Computational Mathematics 4 International Journal of Computer Mathematics 3 Journal of Mathematical Analysis and Applications 3 Journal of Nanjing University. Natural Sciences 3 Applied Mathematics Letters 3 Numerical Mathematics 2 Physics Letters. A 2 BIT 2 Mathematica Numerica Sinica 2 SIAM Journal on Scientific Computing 1 IMA Journal of Numerical Analysis 1 Journal of Mathematical Physics 1 Computing 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 SIAM Journal on Numerical Analysis 1 Applied Mathematics and Mechanics. (English Edition) 1 Mathematical and Computer Modelling 1 Numerical Linear Algebra with Applications 1 Advances in Computational Mathematics 1 Foundations of Computational Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Iranian Journal of Fuzzy Systems 1 Journal of Physics A: Mathematical and Theoretical 1 Communications in Computational Physics 1 Numerical Mathematics: Theory, Methods and Applications all top 5 Fields 164 Numerical analysis (65-XX) 63 Ordinary differential equations (34-XX) 19 Dynamical systems and ergodic theory (37-XX) 18 Partial differential equations (35-XX) 6 Mechanics of particles and systems (70-XX) 3 Operations research, mathematical programming (90-XX) 2 Field theory and polynomials (12-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 130 Publications have been cited 1,618 times in 622 Documents Cited by ▼ Year ▼ A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems. Zbl 1344.65060Fang, Yonglei; Wu, Xinyuan 82 2007 Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems. Zbl 1341.65029Wang, Bin; Iserles, Arieh; Wu, Xinyuan 64 2016 ERKN integrators for systems of oscillatory second-order differential equations. Zbl 1217.65141Wu, Xinyuan; You, Xiong; Shi, Wei; Wang, Bin 62 2010 A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions. Zbl 1136.65068Fang, Yonglei; Wu, Xinyuan 60 2008 Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations. Zbl 1353.65074Wang, Bin; Wu, Xinyuan; Meng, Fanwei 56 2017 Order conditions for ARKN methods solving oscillatory systems. Zbl 1197.65084Wu, Xinyuan; You, Xiong; Xia, Jianlin 54 2009 Extended RKN-type methods for numerical integration of perturbed oscillators. Zbl 1197.65088Yang, Hongli; Wu, Xinyuan; You, Xiong; Fang, Yonglei 48 2009 Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods. Zbl 1258.65068Wu, Xinyuan; Wang, Bin; Xia, Jianlin 43 2012 Efficient energy-preserving integrators for oscillatory Hamiltonian systems. Zbl 1291.65363Wu, Xinyuan; Wang, Bin; Shi, Wei 42 2013 A new continuation Newton-like method and its deformation. Zbl 1023.65043Wu, Xinyuan 41 2000 Structure-preserving algorithms for oscillatory differential equations. Zbl 1276.65041Wu, Xinyuan; You, Xiong; Wang, Bin 36 2013 A new high precision energy-preserving integrator for system of oscillatory second-order differential equations. Zbl 1255.70013Wang, Bin; Wu, Xinyuan 36 2012 New high-order convergence iteration methods without employing derivatives for solving nonlinear equations. Zbl 0985.65047Wu, Xinyuan; Fu, Dongsheng 33 2001 Multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems. Zbl 1217.65140Wu, Xinyuan; Wang, Bin 30 2010 Trigonometrically-fitted ARKN methods for perturbed oscillators. Zbl 1153.65073Yang, Hongli; Wu, Xinyuan 29 2008 Two-step extended RKN methods for oscillatory systems. Zbl 1261.65078Li, Jiyong; Wang, Bin; You, Xiong; Wu, Xinyuan 29 2011 Functionally fitted energy-preserving methods for solving oscillatory nonlinear Hamiltonian systems. Zbl 1342.65231Li, Yu-Wen; Wu, Xinyuan 27 2016 Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems. Zbl 1342.65230Li, Yu-Wen; Wu, Xinyuan 25 2016 Recent developments in structure-preserving algorithms for oscillatory differential equations. Zbl 1444.65003Wu, Xinyuan; Wang, Bin 25 2018 On a class of quadratic convergence iteration formulae without derivatives. Zbl 1023.65042Wu, Xinyuan; Wu, Hongwei 25 2000 A Filon-type asymptotic approach to solving highly oscillatory second-order initial value problems. Zbl 1349.65219Wang, Bin; Liu, Kai; Wu, Xinyuan 24 2013 Two low accuracy methods for stiff systems. Zbl 1024.65053Wu, Xin-Yuan; Xia, Jian-Lin 24 2001 A sixth-order \(A\)-stable explicit one-step method for stiff systems. Zbl 0999.65066Wu, Xinyuan 22 1998 Exponential Fourier collocation methods for solving first-order differential equations. Zbl 1413.65309Wang, Bin; Wu, Xinyuan; Meng, Fanwei; Fang, Yonglei 21 2017 Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems. Zbl 1415.65277Mei, Lijie; Wu, Xinyuan 21 2017 A robust trigonometrically fitted embedded pair for perturbed oscillators. Zbl 1168.65362Fang, Yonglei; Song, Yongzhong; Wu, Xinyuan 20 2009 Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations. Zbl 1380.65052Liu, Changying; Iserles, Arieh; Wu, Xinyuan 19 2018 Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations. Zbl 1284.65186Shi, Wei; Wu, Xinyuan; Xia, Jianlin 19 2012 Quadratically convergent multiple roots finding method without derivatives. Zbl 0985.65048Wu, Xin-Yuan; Xia, Jian-Lin; Shao, Rong 19 2001 A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators. Zbl 1121.65332Fang, Yonglei; Wu, Xinyuan 18 2007 Order conditions for RKN methods solving general second-order oscillatory systems. Zbl 1292.65083You, Xiong; Zhao, Jinxi; Yang, Hongli; Fang, Yonglei; Wu, Xinyuan 18 2014 General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs. Zbl 1349.65518Li, Yu-Wen; Wu, Xinyuan 16 2015 The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications. Zbl 1379.35189Liu, Changying; Wu, Xinyuan 15 2017 The vector form of a sixth-order \(A\)-stable explicit one-step method for stiff problems. Zbl 0954.65059Wu, Xinyuan; Xia, Jianlin 15 2000 An improved regula falsi method with quadratic convergence of both diameter and point for enclosing simple zeros of nonlinear equations. Zbl 1027.65061Wu, Xinyuan; Shen, Zuhe; Xia, Jianlin 15 2003 Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations. Zbl 1380.65205Liu, Changying; Wu, Xinyuan 15 2017 An extended discrete gradient formula for oscillatory Hamiltonian systems. Zbl 1387.65129Liu, Kai; Shi, Wei; Wu, Xinyuan 14 2013 Novel improved multidimensional Störmer-Verlet formulas with applications to four aspects in scientific computation. Zbl 1305.65169Wang, Bin; Wu, Xinyuan; Zhao, Hua 13 2013 The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein-Gordon equations. Zbl 1496.65188Wang, Bin; Wu, Xinyuan 13 2019 New iterative improvement of a solution for an ill-conditioned system of linear equations based on a linear dynamic system. Zbl 1035.65040Wu, Xinyuan; Shao, Rong; Zhu, Yiran 13 2002 A note on stability of multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems. Zbl 1349.65232Wu, Xinyuan 13 2012 Adapted Falkner-type methods solving oscillatory second-order differential equations. Zbl 1267.65088Li, Jiyong; Wu, Xinyuan 13 2013 Structure-preserving algorithms for oscillatory differential equations II. Zbl 1352.65187Wu, Xinyuan; Liu, Kai; Shi, Wei 12 2015 An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations. Zbl 1339.65130Liu, Changying; Shi, Wei; Wu, Xinyuan 11 2014 Energy-preserving continuous stage extended Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems. Zbl 1448.65266Li, Jiyong; Wu, Xinyuan 11 2019 Functionally-fitted energy-preserving integrators for Poisson systems. Zbl 1398.65337Wang, Bin; Wu, Xinyuan 11 2018 ERKN methods for long-term integration of multidimensional orbital problems. Zbl 1349.65233Wu, Xinyuan; Wang, Bin; Liu, Kai; Zhao, Hua 11 2013 An analytical expression of solutions to nonlinear wave equations in higher dimensions with Robin boundary conditions. Zbl 1311.65131Wu, Xinyuan; Mei, Lijie; Liu, Changying 11 2015 Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations. Zbl 1302.65166Wang, Bin; Wu, Xinyuan; Xia, Jianlin 10 2013 A two-step explicit \(P\)-stable method for solving second order initial value problems. Zbl 1042.65056Li, Qinghong; Wu, Xinyuan 10 2003 Extended Runge-Kutta-like formulae. Zbl 1104.65075Wu, Xinyuan; Xia, Jianlin 10 2006 Error analysis of explicit TSERKN methods for highly oscillatory systems. Zbl 1293.65109Li, Jiyong; Wu, Xinyuan 10 2014 On symplectic and symmetric ARKN methods. Zbl 1356.65243Shi, Wei; Wu, Xinyuan 10 2012 Trigonometrically fitted explicit Numerov-type method for periodic IVPs with two frequencies. Zbl 1197.65085Fang, Yonglei; Song, Yongzhong; Wu, Xinyuan 10 2008 Note on the improvement of Newton’s method for system of nonlinear equations. Zbl 1243.65058Wu, Xinyuan 9 2007 A two-step explicit \(P\)-stable method of high phase-lag order for second order IVPs. Zbl 1053.65052Li, Qinghong; Wu, Xinyuan 9 2004 An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations. Zbl 1381.35105Liu, Changying; Wu, Xinyuan 8 2016 An explicit two-step method exact for the scalar test equation \(y'= \lambda y\). Zbl 0951.65065Wu, Xin-Yuan; Xia, Jian-Lin 8 2000 A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems. Zbl 1348.65110Yang, Hongli; Zeng, Xianyang; Wu, Xinyuan; Ru, Zhengliang 8 2014 Effective integrators for nonlinear second-order oscillatory systems with a time-dependent frequency matrix. Zbl 1426.65204Wu, Xinyuan; Wang, Bin; Shi, Wei 7 2013 Global error bounds of one-stage extended RKN integrators for semilinear wave equations. Zbl 1422.65229Wang, Bin; Wu, Xinyuan 7 2019 Multidimensional ARKN methods for general oscillatory second-order initial value problems. Zbl 1352.65183Liu, Kai; Wu, Xinyuan 7 2014 A free-derivative iteration method of order three having convergence of both point and interval for nonlinear equations. Zbl 1030.65047Zhu, Yiran; Wu, Xinyuan 7 2003 Reproducing kernel functions based univariate spline interpolation. Zbl 07413898Geng, Fazhan; Wu, Xinyuan 7 2021 A new framework for solving partial differential equations using semi-analytical explicit RK(N)-type integrators. Zbl 1332.65152Wu, Xinyuan; Liu, Changying; Mei, Lijie 6 2016 An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations with its applications. Zbl 1339.35296Wu, Xinyuan; Liu, Changying 6 2016 Long-time momentum and actions behaviour of energy-preserving methods for semi-linear wave equations via spatial spectral semi-discretisations. Zbl 1437.65152Wang, Bin; Wu, Xinyuan 6 2019 A class of Runge-Kutta formulae of order three and four with reduced evaluations of function. Zbl 1032.65077Wu, Xinyuan 6 2003 Improved Muller method and bisection method with global and asymptotic superlinear convergence of both point and interval for solving nonlinear equations. Zbl 1078.65038Wu, Xinyuan 6 2005 A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems. Zbl 1472.65159Wang, Bin; Wu, Xinyuan 6 2021 A linearly-fitted conservative (dissipative) scheme for efficiently solving conservative (dissipative) nonlinear wave PDEs. Zbl 1413.65369Liu, Kai; Wu, Xinyuan; Shi, Wei 5 2017 Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs. Zbl 1459.65106Wu, Xinyuan; Wang, Bin; Mei, Lijie 5 2021 An improved tri-coloured rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems. Zbl 1376.65106Zeng, Xianyang; Yang, Hongli; Wu, Xinyuan 5 2017 An effective predictor-corrector process for large scale linear system of equations. Zbl 1105.65032Wu, Xinyuan 5 2006 A highly accurate explicit symplectic ERKN method for multi-frequency and multidimensional oscillatory Hamiltonian systems. Zbl 1291.65362Wang, Bin; Wu, Xinyuan 5 2014 Explicit multi-frequency symmetric extended RKN integrators for solving multi-frequency and multidimensional oscillatory reversible systems. Zbl 1329.65155Wang, Bin; Wu, Xinyuan 4 2015 The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications. Zbl 1415.65161Mei, Lijie; Wu, Xinyuan 4 2016 An energy-preserving algorithm for nonlinear Hamiltonian wave equations with Neumann boundary conditions. Zbl 1395.65090Shi, Wei; Liu, Kai; Wu, Xinyuan; Liu, Changying 4 2017 Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations. Zbl 1436.65197Liu, Changying; Wu, Xinyuan 4 2020 A significant improvement on Newton’s iterative method. Zbl 0940.65047Wu, Xinyuan 4 1999 A note on symplectic and symmetric ARKN methods. Zbl 1349.65218Shi, Wei; Wu, Xinyuan 4 2013 Improved filon-type asymptotic methods for highly oscillatory differential equations with multiple time scales. Zbl 1349.65229Wang, Bin; Wu, Xinyuan 4 2014 New vector forms of elemental functions with Taylor series. Zbl 1043.65082Wu, Xin-Yuan; Xia, Jian-Lin 4 2003 A two-step explicit \(P\)-stable method of high phase-lag order for linear periodic IVPs. Zbl 1111.65068Li, Qinghong; Wu, Xinyuan 4 2007 Note on global convergence of ODE methods for unconstrained optimization. Zbl 1032.90047Wu, Xinyuan; Xia, Jianlin; Ouyang, Zixiang 4 2002 A two-step symmetric method for charged-particle dynamics in a normal or strong magnetic field. Zbl 1448.65067Wang, Bin; Wu, Xinyuan; Fang, Yonglei 4 2020 Wilkinson’s iterative refinement of solution with automatic step-size control for linear system of equations. Zbl 1193.65033Wu, Xinyuan; Fang, Yonglei 4 2007 Error analysis of a new transformation for multiple zeros finding free from derivative evaluations. Zbl 1050.65053Wu, Xin-Yuan; Xia, Jianlin 4 2003 A note on computational algorithm for the inverse of a square matrix. Zbl 1121.65027Wu, Xinyuan 4 2007 New embedded pairs of explicit Runge-Kutta methods with FSAL properties adapted to the numerical integration of oscillatory problems. Zbl 1225.65072Fang, Yonglei; Song, Yongzhong; Wu, Xinyuan 4 2008 The existence of explicit symplectic ARKN methods with several stages and algebraic order greater than two. Zbl 1433.65340Li, Jiyong; Shi, Wei; Wu, Xinyuan 3 2019 A symplectic approximation with nonlinear stability and convergence analysis for efficiently solving semi-linear Klein-Gordon equations. Zbl 1439.35417Wang, Bin; Wu, Xinyuan 3 2019 Exponential collocation methods for conservative or dissipative systems. Zbl 1418.65093Wang, Bin; Wu, Xinyuan 3 2019 Some substantial modifications and improvements for derivative-free iterative methods and derivative-free transformation for multiple zeros. Zbl 1170.65315Wu, Xinyuan; Xia, Jianlin 3 2006 Iterative refinement of solution with biparameter for solving ill-conditioned systems of linear algebraic equations. Zbl 1034.65025Wu, Xin-yuan; Shao, Rong; Xue, Guo-he 3 2002 Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral. Zbl 07422794Geng, F. Z.; Wu, X. Y. 3 2021 Comments on “Embedded pair of extended Runge-Kutta-Nyström type methods for perturbed oscillators”. Zbl 1201.65127Wu, Xinyuan; Wang, Bin 3 2010 Two-step Runge-Kutta methods of order over five with reduced function evaluations. Zbl 1061.65069Wu, Xinyuan 3 2004 A class of two-step explicit methods for periodic IVPs. Zbl 1095.65064Li, Qinghong; Wu, Xinyuan 2 2005 New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions. Zbl 1429.65189Liu, Changying; Wu, Xinyuan; Shi, Wei 2 2018 Energy-preserving continuous-stage exponential Runge-Kutta integrators for efficiently solving Hamiltonian systems. Zbl 1492.65188Mei, Lijie; Huang, Li; Wu, Xinyuan 2 2022 A unified framework for the study of high-order energy-preserving integrators for solving Poisson systems. Zbl 07517110Mei, Lijie; Huang, Li; Wu, Xinyuan 1 2022 A novel kernel functions algorithm for solving impulsive boundary value problems. Zbl 07590665Geng, F. Z.; Wu, X. Y. 1 2022 Reproducing kernel functions based univariate spline interpolation. Zbl 07413898Geng, Fazhan; Wu, Xinyuan 7 2021 A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems. Zbl 1472.65159Wang, Bin; Wu, Xinyuan 6 2021 Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs. Zbl 1459.65106Wu, Xinyuan; Wang, Bin; Mei, Lijie 5 2021 Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral. Zbl 07422794Geng, F. Z.; Wu, X. Y. 3 2021 Continuous trigonometric collocation polynomial approximations with geometric and superconvergence analysis for efficiently solving semi-linear highly oscillatory hyperbolic systems. Zbl 1471.65072Liu, Changying; Wu, Xinyuan 2 2021 Geometric integrators for differential equations with highly oscillatory solutions. Zbl 07384483Wu, Xinyuan; Wang, Bin 2 2021 Energy-preserving exponential integrators of arbitrarily high order for conservative or dissipative systems with highly oscillatory solutions. Zbl 07513793Mei, Lijie; Huang, Li; Wu, Xinyuan 1 2021 Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations. Zbl 1436.65197Liu, Changying; Wu, Xinyuan 4 2020 A two-step symmetric method for charged-particle dynamics in a normal or strong magnetic field. Zbl 1448.65067Wang, Bin; Wu, Xinyuan; Fang, Yonglei 4 2020 A continuous-stage modified leap-frog scheme for high-dimensional semi-linear Hamiltonian wave equations. Zbl 1463.65407Wang, Bin; Wu, Xinyuan; Fang, Yonglei 2 2020 A new quadratic deviation of fuzzy random variable and its application to portfolio optimization. Zbl 1458.91200Wu, X.; Ralescu, D. A.; Liu, Y. 1 2020 The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein-Gordon equations. Zbl 1496.65188Wang, Bin; Wu, Xinyuan 13 2019 Energy-preserving continuous stage extended Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems. Zbl 1448.65266Li, Jiyong; Wu, Xinyuan 11 2019 Global error bounds of one-stage extended RKN integrators for semilinear wave equations. Zbl 1422.65229Wang, Bin; Wu, Xinyuan 7 2019 Long-time momentum and actions behaviour of energy-preserving methods for semi-linear wave equations via spatial spectral semi-discretisations. Zbl 1437.65152Wang, Bin; Wu, Xinyuan 6 2019 The existence of explicit symplectic ARKN methods with several stages and algebraic order greater than two. Zbl 1433.65340Li, Jiyong; Shi, Wei; Wu, Xinyuan 3 2019 A symplectic approximation with nonlinear stability and convergence analysis for efficiently solving semi-linear Klein-Gordon equations. Zbl 1439.35417Wang, Bin; Wu, Xinyuan 3 2019 Exponential collocation methods for conservative or dissipative systems. Zbl 1418.65093Wang, Bin; Wu, Xinyuan 3 2019 Volume-preserving exponential integrators and their applications. Zbl 1452.37083Wang, Bin; Wu, Xinyuan 2 2019 Numerical analysis of an energy-conservation scheme for two-dimensional Hamiltonian wave equations with Neumann boundary conditions. Zbl 1407.35008Liu, Changying; Shi, Wei; Wu, Xinyuan 2 2019 Explicit Gautschi-type integrators for nonlinear multi-frequency oscillatory second-order initial value problems. Zbl 1418.65077Shi, Wei; Wu, Xinyuan 1 2019 Recent developments in structure-preserving algorithms for oscillatory differential equations. Zbl 1444.65003Wu, Xinyuan; Wang, Bin 25 2018 Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations. Zbl 1380.65052Liu, Changying; Iserles, Arieh; Wu, Xinyuan 19 2018 Functionally-fitted energy-preserving integrators for Poisson systems. Zbl 1398.65337Wang, Bin; Wu, Xinyuan 11 2018 New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions. Zbl 1429.65189Liu, Changying; Wu, Xinyuan; Shi, Wei 2 2018 Extended phase properties and stability analysis of RKN-type integrators for solving general oscillatory second-order initial value problems. Zbl 1381.65053Liu, Kai; Wu, Xinyuan; Shi, Wei 1 2018 Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations. Zbl 1353.65074Wang, Bin; Wu, Xinyuan; Meng, Fanwei 56 2017 Exponential Fourier collocation methods for solving first-order differential equations. Zbl 1413.65309Wang, Bin; Wu, Xinyuan; Meng, Fanwei; Fang, Yonglei 21 2017 Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems. Zbl 1415.65277Mei, Lijie; Wu, Xinyuan 21 2017 The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications. Zbl 1379.35189Liu, Changying; Wu, Xinyuan 15 2017 Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations. Zbl 1380.65205Liu, Changying; Wu, Xinyuan 15 2017 A linearly-fitted conservative (dissipative) scheme for efficiently solving conservative (dissipative) nonlinear wave PDEs. Zbl 1413.65369Liu, Kai; Wu, Xinyuan; Shi, Wei 5 2017 An improved tri-coloured rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems. Zbl 1376.65106Zeng, Xianyang; Yang, Hongli; Wu, Xinyuan 5 2017 An energy-preserving algorithm for nonlinear Hamiltonian wave equations with Neumann boundary conditions. Zbl 1395.65090Shi, Wei; Liu, Kai; Wu, Xinyuan; Liu, Changying 4 2017 An essential extension of the finite-energy condition for extended Runge-Kutta-Nyström integrators when applied to nonlinear wave equations. Zbl 1488.65177Mei, Lijie; Liu, Changying; Wu, Xinyuan 1 2017 Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems. Zbl 1341.65029Wang, Bin; Iserles, Arieh; Wu, Xinyuan 64 2016 Functionally fitted energy-preserving methods for solving oscillatory nonlinear Hamiltonian systems. Zbl 1342.65231Li, Yu-Wen; Wu, Xinyuan 27 2016 Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems. Zbl 1342.65230Li, Yu-Wen; Wu, Xinyuan 25 2016 An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations. Zbl 1381.35105Liu, Changying; Wu, Xinyuan 8 2016 A new framework for solving partial differential equations using semi-analytical explicit RK(N)-type integrators. Zbl 1332.65152Wu, Xinyuan; Liu, Changying; Mei, Lijie 6 2016 An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations with its applications. Zbl 1339.35296Wu, Xinyuan; Liu, Changying 6 2016 The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications. Zbl 1415.65161Mei, Lijie; Wu, Xinyuan 4 2016 General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs. Zbl 1349.65518Li, Yu-Wen; Wu, Xinyuan 16 2015 Structure-preserving algorithms for oscillatory differential equations II. Zbl 1352.65187Wu, Xinyuan; Liu, Kai; Shi, Wei 12 2015 An analytical expression of solutions to nonlinear wave equations in higher dimensions with Robin boundary conditions. Zbl 1311.65131Wu, Xinyuan; Mei, Lijie; Liu, Changying 11 2015 Explicit multi-frequency symmetric extended RKN integrators for solving multi-frequency and multidimensional oscillatory reversible systems. Zbl 1329.65155Wang, Bin; Wu, Xinyuan 4 2015 High-order symplectic and symmetric composition methods for multi-frequency and multi-dimensional oscillatory Hamiltonian systems. Zbl 1340.65307Liu, Kai; Wu, Xinyuan 1 2015 Order conditions for RKN methods solving general second-order oscillatory systems. Zbl 1292.65083You, Xiong; Zhao, Jinxi; Yang, Hongli; Fang, Yonglei; Wu, Xinyuan 18 2014 An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations. Zbl 1339.65130Liu, Changying; Shi, Wei; Wu, Xinyuan 11 2014 Error analysis of explicit TSERKN methods for highly oscillatory systems. Zbl 1293.65109Li, Jiyong; Wu, Xinyuan 10 2014 A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems. Zbl 1348.65110Yang, Hongli; Zeng, Xianyang; Wu, Xinyuan; Ru, Zhengliang 8 2014 Multidimensional ARKN methods for general oscillatory second-order initial value problems. Zbl 1352.65183Liu, Kai; Wu, Xinyuan 7 2014 A highly accurate explicit symplectic ERKN method for multi-frequency and multidimensional oscillatory Hamiltonian systems. Zbl 1291.65362Wang, Bin; Wu, Xinyuan 5 2014 Improved filon-type asymptotic methods for highly oscillatory differential equations with multiple time scales. Zbl 1349.65229Wang, Bin; Wu, Xinyuan 4 2014 Efficient energy-preserving integrators for oscillatory Hamiltonian systems. Zbl 1291.65363Wu, Xinyuan; Wang, Bin; Shi, Wei 42 2013 Structure-preserving algorithms for oscillatory differential equations. Zbl 1276.65041Wu, Xinyuan; You, Xiong; Wang, Bin 36 2013 A Filon-type asymptotic approach to solving highly oscillatory second-order initial value problems. Zbl 1349.65219Wang, Bin; Liu, Kai; Wu, Xinyuan 24 2013 An extended discrete gradient formula for oscillatory Hamiltonian systems. Zbl 1387.65129Liu, Kai; Shi, Wei; Wu, Xinyuan 14 2013 Novel improved multidimensional Störmer-Verlet formulas with applications to four aspects in scientific computation. Zbl 1305.65169Wang, Bin; Wu, Xinyuan; Zhao, Hua 13 2013 Adapted Falkner-type methods solving oscillatory second-order differential equations. Zbl 1267.65088Li, Jiyong; Wu, Xinyuan 13 2013 ERKN methods for long-term integration of multidimensional orbital problems. Zbl 1349.65233Wu, Xinyuan; Wang, Bin; Liu, Kai; Zhao, Hua 11 2013 Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations. Zbl 1302.65166Wang, Bin; Wu, Xinyuan; Xia, Jianlin 10 2013 Effective integrators for nonlinear second-order oscillatory systems with a time-dependent frequency matrix. Zbl 1426.65204Wu, Xinyuan; Wang, Bin; Shi, Wei 7 2013 A note on symplectic and symmetric ARKN methods. Zbl 1349.65218Shi, Wei; Wu, Xinyuan 4 2013 Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods. Zbl 1258.65068Wu, Xinyuan; Wang, Bin; Xia, Jianlin 43 2012 A new high precision energy-preserving integrator for system of oscillatory second-order differential equations. Zbl 1255.70013Wang, Bin; Wu, Xinyuan 36 2012 Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations. Zbl 1284.65186Shi, Wei; Wu, Xinyuan; Xia, Jianlin 19 2012 A note on stability of multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems. Zbl 1349.65232Wu, Xinyuan 13 2012 On symplectic and symmetric ARKN methods. Zbl 1356.65243Shi, Wei; Wu, Xinyuan 10 2012 On extended RKN integrators for multidimensional perturbed oscillators with applications. Zbl 1243.65088Wu, Xinyuan; Wang, Bin; Shi, Wei; You, Xiong 1 2012 Two-step extended RKN methods for oscillatory systems. Zbl 1261.65078Li, Jiyong; Wang, Bin; You, Xiong; Wu, Xinyuan 29 2011 A new iterative refinement with roundoff error analysis. Zbl 1249.65058Wu, Xinyuan; Wang, Zhengyu 1 2011 ERKN integrators for systems of oscillatory second-order differential equations. Zbl 1217.65141Wu, Xinyuan; You, Xiong; Shi, Wei; Wang, Bin 62 2010 Multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems. Zbl 1217.65140Wu, Xinyuan; Wang, Bin 30 2010 Comments on “Embedded pair of extended Runge-Kutta-Nyström type methods for perturbed oscillators”. Zbl 1201.65127Wu, Xinyuan; Wang, Bin 3 2010 Extended RKN-type methods with minimal dispersion error for perturbed oscillators. Zbl 1208.65096Fang, Yonglei; Ming, Qinghe; Wu, Xinyuan 2 2010 Extended version with the analysis of dynamic system for iterative refinement of solution. Zbl 1192.65046Wu, Xinyuan; You, Xiong 2 2010 Extended RKN methods with FSAL property for oscillatory systems. Zbl 1215.65123Fang, Yonglei; Li, Qinghong; Wu, Xinyuan 1 2010 Order conditions for ARKN methods solving oscillatory systems. Zbl 1197.65084Wu, Xinyuan; You, Xiong; Xia, Jianlin 54 2009 Extended RKN-type methods for numerical integration of perturbed oscillators. Zbl 1197.65088Yang, Hongli; Wu, Xinyuan; You, Xiong; Fang, Yonglei 48 2009 A robust trigonometrically fitted embedded pair for perturbed oscillators. Zbl 1168.65362Fang, Yonglei; Song, Yongzhong; Wu, Xinyuan 20 2009 A semi-local convergence theorem for a robust revised Newton’s method. Zbl 1189.65096Wang, Zhengyu; Wu, Xinyuan 2 2009 Piecewise integration of differential variational inequality. Zbl 1182.65102Wang, Zhengyu; Wu, Xinyuan 1 2009 A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions. Zbl 1136.65068Fang, Yonglei; Wu, Xinyuan 60 2008 Trigonometrically-fitted ARKN methods for perturbed oscillators. Zbl 1153.65073Yang, Hongli; Wu, Xinyuan 29 2008 Trigonometrically fitted explicit Numerov-type method for periodic IVPs with two frequencies. Zbl 1197.65085Fang, Yonglei; Song, Yongzhong; Wu, Xinyuan 10 2008 New embedded pairs of explicit Runge-Kutta methods with FSAL properties adapted to the numerical integration of oscillatory problems. Zbl 1225.65072Fang, Yonglei; Song, Yongzhong; Wu, Xinyuan 4 2008 A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems. Zbl 1344.65060Fang, Yonglei; Wu, Xinyuan 82 2007 A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators. Zbl 1121.65332Fang, Yonglei; Wu, Xinyuan 18 2007 Note on the improvement of Newton’s method for system of nonlinear equations. Zbl 1243.65058Wu, Xinyuan 9 2007 A two-step explicit \(P\)-stable method of high phase-lag order for linear periodic IVPs. Zbl 1111.65068Li, Qinghong; Wu, Xinyuan 4 2007 Wilkinson’s iterative refinement of solution with automatic step-size control for linear system of equations. Zbl 1193.65033Wu, Xinyuan; Fang, Yonglei 4 2007 A note on computational algorithm for the inverse of a square matrix. Zbl 1121.65027Wu, Xinyuan 4 2007 Newton-like method with some remarks. Zbl 1121.65053Wu, Xinyuan 2 2007 Order conditions for integrators and mappings with applications. Zbl 1128.65059Wu, Xinyuan 1 2007 Extended Runge-Kutta-like formulae. Zbl 1104.65075Wu, Xinyuan; Xia, Jianlin 10 2006 An effective predictor-corrector process for large scale linear system of equations. Zbl 1105.65032Wu, Xinyuan 5 2006 ...and 30 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 630 Authors 103 Wu, Xinyuan 80 Simos, Theodore E. 45 Wang, Bin 33 You, Xiong 32 Fang, Yonglei 25 Li, Jiyong 23 Alolyan, Ibraheem 21 Shi, Wei 17 Liu, Changying 14 Jator, Samuel N. 14 Liu, Kai 13 Lin, Chialiang 13 Wang, Yushun 12 Ramos, Higinio 12 Xia, Jianlin 11 Medvedev, Maxim A. 10 Chun, Changbum 10 Mei, Lijie 9 Cai, Wenjun 9 Jiang, Chaolong 9 Li, Qinghong 9 Yang, Hongli 8 Ehigie, Julius Osato 8 Okunuga, Solomon A. 7 Medvedeva, Marina A. 7 Song, Yongzhong 7 Yang, Yanping 6 Brugnano, Luigi 6 Kanwar, Vinay 6 Li, Ting 6 Ma, Changfeng 6 Rández, Luis 6 Wang, Xianfen 6 Xu, Zhuangzhi 5 Cai, Jiaxiang 5 Chen, Jinhai 5 Chen, Zhaoxia 5 Deng, Shuo 5 Franco, J. Méndez 5 Iavernaro, Felice 5 Kou, Jisheng 5 Liu, Zhongli 5 Ming, Qinghe 5 Qian, Xu 5 Senu, Norazak 5 Song, Songhe 5 Tang, Xiao-Bin 5 Tian, Hongjiong 5 Vigo-Aguiar, Jesus 5 Wang, Xiang 5 Zeng, Xianyang 4 Abdulganiy, Ridwanulahi Iyanda 4 Ahmad, Fayyaz 4 Berg, Dmitry B. 4 Ebadi, Moosa 4 Fu, Yayun 4 Gong, Yuezheng 4 Huang, Li 4 Li, Chengliang 4 Li, Yitian 4 Liang, Dong 4 Meng, Fanwei 4 Wang, Haijun 4 Yun, Beong In 4 Zhang, Ruqiang 4 Zhao, Longbin 4 Zheng, Juan 3 Bhatia, Saurabh 3 Cui, Jin 3 D’Ambrosio, Raffaele 3 Feng, Xinlong 3 Fu, Ting 3 Gokhale, Mukund Y. 3 Hou, Xilin 3 Hu, Dongdong 3 Huang, Chengming 3 Ibrahim, Zarina Bibi Binti 3 Iserles, Arieh 3 Ismail, Fudziah Bt. 3 Khalsaraei, Mohammad Mehdizadeh 3 Khojasteh Salkuyeh, Davod 3 Li, Dongfang 3 Li, Weiguo 3 Li, Yu 3 Liu, Shiwei 3 Montijano, Juan Ignacio 3 Ngwane, Fidele F. 3 Niu, Jing 3 Singh, Arvind Kumar 3 Singh, Gurjinder 3 Singh, Manoj Kumar 3 Tang, Wensheng 3 Ullah, Malik Zaka 3 Wang, Xiuhua 3 Wang, Zenggui 3 Wu, Yajun 3 Xu, Yang 3 Yang, Jie 3 Zhao, Jingjun 2 Ahmad, Rokiah Rozita ...and 530 more Authors all top 5 Cited in 103 Serials 97 Applied Mathematics and Computation 87 Journal of Mathematical Chemistry 40 Numerical Algorithms 39 Applied Numerical Mathematics 33 Journal of Computational and Applied Mathematics 26 International Journal of Computer Mathematics 24 Journal of Computational Physics 23 Applied Mathematics Letters 17 Computers & Mathematics with Applications 14 Computer Physics Communications 11 Journal of Scientific Computing 10 Calcolo 10 Mathematical Problems in Engineering 9 Computational and Applied Mathematics 8 Applied Mathematical Modelling 7 SIAM Journal on Scientific Computing 7 Journal of Applied Mathematics and Computing 6 BIT 6 Mathematics and Computers in Simulation 6 Algorithms 6 International Journal of Applied and Computational Mathematics 5 Advances in Computational Mathematics 5 Advances in Difference Equations 5 Afrika Matematika 4 Journal of the Nigerian Mathematical Society 4 Discrete and Continuous Dynamical Systems. 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Second Series 1 International Journal of Computational Methods 1 Boundary Value Problems 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Journal of Fixed Point Theory and Applications 1 Communications in Computational Physics 1 European Journal of Pure and Applied Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Asian-European Journal of Mathematics 1 ACM Communications in Computer Algebra 1 Science China. Mathematics 1 Journal of the Korean Society for Industrial and Applied Mathematics 1 Axioms 1 Mathematical Sciences 1 Journal of Mathematics 1 Journal of Linear and Topological Algebra 1 AMM. Applied Mathematics and Mechanics. (English Edition) ...and 3 more Serials all top 5 Cited in 36 Fields 578 Numerical analysis (65-XX) 148 Ordinary differential equations (34-XX) 96 Partial differential equations (35-XX) 47 Quantum theory (81-XX) 43 Dynamical systems and ergodic theory (37-XX) 12 Biology and other natural sciences (92-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Operations research, mathematical programming (90-XX) 9 Optics, electromagnetic theory (78-XX) 7 Real functions (26-XX) 7 Probability theory and stochastic processes (60-XX) 7 Fluid mechanics (76-XX) 6 Approximations and expansions (41-XX) 6 Systems theory; control (93-XX) 5 Mechanics of particles and systems (70-XX) 5 Statistical mechanics, structure of matter (82-XX) 5 Information and communication theory, circuits (94-XX) 4 Functions of a complex variable (30-XX) 4 Integral equations (45-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Special functions (33-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Field theory and polynomials (12-XX) 2 Difference and functional equations (39-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Measure and integration (28-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX) Citations by Year