Shi, Wei; Liu, Kai A dissipation-preserving integrator for damped oscillatory Hamiltonian systems. (English) Zbl 1499.65294 J. Comput. Math. 40, No. 4, 573-591 (2022). MSC: 65L05 65L07 65L20 65P10 PDFBibTeX XMLCite \textit{W. Shi} and \textit{K. Liu}, J. Comput. Math. 40, No. 4, 573--591 (2022; Zbl 1499.65294) Full Text: DOI
Liu, Kai; Zhang, Mingqian; Shi, Wei; Yang, Jie A new Jacobi-type iteration method for solving M-matrix or nonnegative linear systems. (English) Zbl 1480.65073 Japan J. Ind. Appl. Math. 39, No. 1, 403-417 (2022). MSC: 65F10 65L05 65L07 65L20 65N22 PDFBibTeX XMLCite \textit{K. Liu} et al., Japan J. Ind. Appl. Math. 39, No. 1, 403--417 (2022; Zbl 1480.65073) Full Text: DOI
Liu, Kai; Fu, Ting; Shi, Wei Stability analysis for explicit ERKN methods solving general second-order oscillatory systems. (English) Zbl 07419038 Bull. Malays. Math. Sci. Soc. (2) 44, No. 6, 4143-4154 (2021). MSC: 65L05 65L06 PDFBibTeX XMLCite \textit{K. Liu} et al., Bull. Malays. Math. Sci. Soc. (2) 44, No. 6, 4143--4154 (2021; Zbl 07419038) Full Text: DOI
Liu, Kai; Fu, Ting; Shi, Wei A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting. (English) Zbl 1482.65227 Appl. Numer. Math. 170, 242-254 (2021). MSC: 65P10 65L05 PDFBibTeX XMLCite \textit{K. Liu} et al., Appl. Numer. Math. 170, 242--254 (2021; Zbl 1482.65227) Full Text: DOI
Xie, Jiaquan; Gong, Xiaoyuan; Shi, Wei; Li, Ruili; Zhao, Weici; Wang, Tao Applying the three-dimensional block-pulse functions to solve system of Volterra-Hammerstein integral equations. (English) Zbl 07777665 Numer. Methods Partial Differ. Equations 36, No. 6, 1648-1661 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{J. Xie} et al., Numer. Methods Partial Differ. Equations 36, No. 6, 1648--1661 (2020; Zbl 07777665) Full Text: DOI
Liu, Kai; Yang, Jie; Shi, Wei A new SOR-type iteration method for solving linear systems. (English) Zbl 1440.65117 Appl. Math. Lett. 102, Article ID 106104, 8 p. (2020). MSC: 65M22 65F10 65F35 65L12 PDFBibTeX XMLCite \textit{K. Liu} et al., Appl. Math. Lett. 102, Article ID 106104, 8 p. (2020; Zbl 1440.65117) Full Text: DOI
Shi, Wei; Wu, Xinyuan; Liu, Kai Efficient implementation of the ARKN and ERKN integrators for multi-frequency oscillatory systems with multiple time scales. (English) Zbl 1439.65080 Appl. Numer. Math. 151, 13-26 (2020). MSC: 65L06 65L05 65P10 34C15 PDFBibTeX XMLCite \textit{W. Shi} et al., Appl. Numer. Math. 151, 13--26 (2020; Zbl 1439.65080) Full Text: DOI
Shi, Wei; Wu, Xinyuan Explicit Gautschi-type integrators for nonlinear multi-frequency oscillatory second-order initial value problems. (English) Zbl 1418.65077 Numer. Algorithms 81, No. 4, 1275-1294 (2019). MSC: 65L05 65L06 34C15 65F30 PDFBibTeX XMLCite \textit{W. Shi} and \textit{X. Wu}, Numer. Algorithms 81, No. 4, 1275--1294 (2019; Zbl 1418.65077) Full Text: DOI
Li, Jiyong; Shi, Wei; Wu, Xinyuan The existence of explicit symplectic ARKN methods with several stages and algebraic order greater than two. (English) Zbl 1433.65340 J. Comput. Appl. Math. 353, 204-209 (2019). MSC: 65P10 65L06 37M15 PDFBibTeX XMLCite \textit{J. Li} et al., J. Comput. Appl. Math. 353, 204--209 (2019; Zbl 1433.65340) Full Text: DOI
Liu, Changying; Shi, Wei; Wu, Xinyuan Numerical analysis of an energy-conservation scheme for two-dimensional Hamiltonian wave equations with Neumann boundary conditions. (English) Zbl 1407.35008 Int. J. Numer. Anal. Model. 16, No. 2, 319-339 (2019). MSC: 35A35 35C15 65M06 65M12 65M20 65M70 PDFBibTeX XMLCite \textit{C. Liu} et al., Int. J. Numer. Anal. Model. 16, No. 2, 319--339 (2019; Zbl 1407.35008) Full Text: Link
Liu, Changying; Wu, Xinyuan; Shi, Wei New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions. (English) Zbl 1429.65189 Appl. Math. Comput. 339, 588-606 (2018). MSC: 65M06 35C15 35L20 35L71 PDFBibTeX XMLCite \textit{C. Liu} et al., Appl. Math. Comput. 339, 588--606 (2018; Zbl 1429.65189) Full Text: DOI
Shi, Wei; Liu, Kai A new analytical formula for the wave equations with variable coefficients. (English) Zbl 1524.65260 Appl. Math. Lett. 84, 137-142 (2018). MSC: 65L05 PDFBibTeX XMLCite \textit{W. Shi} and \textit{K. Liu}, Appl. Math. Lett. 84, 137--142 (2018; Zbl 1524.65260) Full Text: DOI
Liu, Kai; Shi, Wei High-order skew-symmetric differentiation matrix on symmetric grid. (English) Zbl 1457.65054 J. Comput. Appl. Math. 343, 206-216 (2018). MSC: 65M06 65M12 65M50 PDFBibTeX XMLCite \textit{K. Liu} and \textit{W. Shi}, J. Comput. Appl. Math. 343, 206--216 (2018; Zbl 1457.65054) Full Text: DOI
Liu, Kai; Wu, Xinyuan; Shi, Wei Extended phase properties and stability analysis of RKN-type integrators for solving general oscillatory second-order initial value problems. (English) Zbl 1381.65053 Numer. Algorithms 77, No. 1, 37-56 (2018). MSC: 65L05 65L06 65L20 34A34 34C10 PDFBibTeX XMLCite \textit{K. Liu} et al., Numer. Algorithms 77, No. 1, 37--56 (2018; Zbl 1381.65053) Full Text: DOI
Liu, Kai; Wu, Xinyuan; Shi, Wei A linearly-fitted conservative (dissipative) scheme for efficiently solving conservative (dissipative) nonlinear wave PDEs. (English) Zbl 1413.65369 J. Comput. Math. 35, No. 6, 780-800 (2017). MSC: 65M60 65P10 PDFBibTeX XMLCite \textit{K. Liu} et al., J. Comput. Math. 35, No. 6, 780--800 (2017; Zbl 1413.65369) Full Text: DOI
Shi, Wei; Liu, Kai; Wu, Xinyuan; Liu, Changying An energy-preserving algorithm for nonlinear Hamiltonian wave equations with Neumann boundary conditions. (English) Zbl 1395.65090 Calcolo 54, No. 4, 1379-1402 (2017). Reviewer: Michael Jung (Dresden) MSC: 65M60 65M12 35Q53 PDFBibTeX XMLCite \textit{W. Shi} et al., Calcolo 54, No. 4, 1379--1402 (2017; Zbl 1395.65090) Full Text: DOI
Chen, Zhaoxia; Zhang, Ruqiang; Shi, Wei; You, Xiong New optimized symmetric and symplectic trigonometrically fitted RKN methods for second-order oscillatory differential equations. (English) Zbl 1373.65047 Int. J. Comput. Math. 94, No. 5, 1036-1061 (2017). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 65L06 65L05 65L12 65P10 37M15 34C10 PDFBibTeX XMLCite \textit{Z. Chen} et al., Int. J. Comput. Math. 94, No. 5, 1036--1061 (2017; Zbl 1373.65047) Full Text: DOI
Wu, Xinyuan; Liu, Kai; Shi, Wei Structure-preserving algorithms for oscillatory differential equations II. (English) Zbl 1352.65187 Berlin: Springer; Beijing: Science Press (ISBN 978-3-662-48155-4/hbk; 978-3-662-48156-1/ebook). xv, 298 p. (2015). Reviewer: Roland Pulch (Greifswald) MSC: 65L05 65-02 65L06 65L70 65P10 34C10 37M15 37J05 PDFBibTeX XMLCite \textit{X. Wu} et al., Structure-preserving algorithms for oscillatory differential equations II. Berlin: Springer; Beijing: Science Press (2015; Zbl 1352.65187) Full Text: DOI
Liu, Changying; Shi, Wei; Wu, Xinyuan An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations. (English) Zbl 1339.65130 Appl. Math. Comput. 246, 696-710 (2014). MSC: 65M06 65M20 PDFBibTeX XMLCite \textit{C. Liu} et al., Appl. Math. Comput. 246, 696--710 (2014; Zbl 1339.65130) Full Text: DOI
Wu, Xinyuan; Wang, Bin; Shi, Wei Effective integrators for nonlinear second-order oscillatory systems with a time-dependent frequency matrix. (English) Zbl 1426.65204 Appl. Math. Modelling 37, No. 9, 6505-6518 (2013). MSC: 65P10 65L05 65L06 70H05 PDFBibTeX XMLCite \textit{X. Wu} et al., Appl. Math. Modelling 37, No. 9, 6505--6518 (2013; Zbl 1426.65204) Full Text: DOI
Shi, Wei; Wu, Xinyuan A note on symplectic and symmetric ARKN methods. (English) Zbl 1349.65218 Comput. Phys. Commun. 184, No. 11, 2408-2411 (2013). MSC: 65P10 65L06 PDFBibTeX XMLCite \textit{W. Shi} and \textit{X. Wu}, Comput. Phys. Commun. 184, No. 11, 2408--2411 (2013; Zbl 1349.65218) Full Text: DOI
Wu, Xinyuan; Wang, Bin; Shi, Wei Efficient energy-preserving integrators for oscillatory Hamiltonian systems. (English) Zbl 1291.65363 J. Comput. Phys. 235, 587-605 (2013). MSC: 65P10 34C15 37M15 PDFBibTeX XMLCite \textit{X. Wu} et al., J. Comput. Phys. 235, 587--605 (2013; Zbl 1291.65363) Full Text: DOI
Liu, Kai; Shi, Wei; Wu, Xinyuan An extended discrete gradient formula for oscillatory Hamiltonian systems. (English) Zbl 1387.65129 J. Phys. A, Math. Theor. 46, No. 16, 165203, 19 p. (2013). MSC: 65P10 37M15 70H05 PDFBibTeX XMLCite \textit{K. Liu} et al., J. Phys. A, Math. Theor. 46, No. 16, 165203, 19 p. (2013; Zbl 1387.65129) Full Text: DOI
Shi, Wei; Wu, Xinyuan; Xia, Jianlin Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations. (English) Zbl 1284.65186 J. Comput. Phys. 231, No. 22, 7671-7694 (2012). MSC: 65P10 37M15 35L65 35L05 PDFBibTeX XMLCite \textit{W. Shi} et al., J. Comput. Phys. 231, No. 22, 7671--7694 (2012; Zbl 1284.65186) Full Text: DOI
Shi, Wei; Wu, Xinyuan On symplectic and symmetric ARKN methods. (English) Zbl 1356.65243 Comput. Phys. Commun. 183, No. 6, 1250-1258 (2012). MSC: 65P10 65L06 PDFBibTeX XMLCite \textit{W. Shi} and \textit{X. Wu}, Comput. Phys. Commun. 183, No. 6, 1250--1258 (2012; Zbl 1356.65243) Full Text: DOI
Chen, Zhaoxia; You, Xiong; Shi, Wei; Liu, Zhongli Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems. (English) Zbl 1266.65201 Comput. Phys. Commun. 183, No. 1, 86-98 (2012). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65P10 37M15 65L06 PDFBibTeX XMLCite \textit{Z. Chen} et al., Comput. Phys. Commun. 183, No. 1, 86--98 (2012; Zbl 1266.65201) Full Text: DOI
Wu, Xinyuan; Wang, Bin; Shi, Wei; You, Xiong On extended RKN integrators for multidimensional perturbed oscillators with applications. (English) Zbl 1243.65088 Appl. Math. Modelling 36, No. 4, 1504-1513 (2012). MSC: 65L06 PDFBibTeX XMLCite \textit{X. Wu} et al., Appl. Math. Modelling 36, No. 4, 1504--1513 (2012; Zbl 1243.65088) Full Text: DOI
Wu, Xinyuan; You, Xiong; Shi, Wei; Wang, Bin ERKN integrators for systems of oscillatory second-order differential equations. (English) Zbl 1217.65141 Comput. Phys. Commun. 181, No. 11, 1873-1887 (2010). MSC: 65L05 PDFBibTeX XMLCite \textit{X. Wu} et al., Comput. Phys. Commun. 181, No. 11, 1873--1887 (2010; Zbl 1217.65141) Full Text: DOI
Shi, Wei; You, Xiong; Wu, Xinyuan Multi-symplectic exponentially fitted RKN methods for wave equations. (English) Zbl 1182.65192 Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics, Rethymno, Crete, Greece, September 18–22, 2009. Vol. 2. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0708-4/hbk; 978-0-7354-0709-1/set). AIP Conference Proceedings 1168, 2, 900-903 (2009). MSC: 65P10 37M15 65L06 35Q53 65M20 65M12 37K10 PDFBibTeX XMLCite \textit{W. Shi} et al., AIP Conf. Proc. 1168, 900--903 (2009; Zbl 1182.65192) Full Text: DOI