Songhe Song

Publication Activity (10 Years)

Years Active: 2002-2024
Publications (10 Years): 35

Top Topics

Boundary Conditions

Differential Equations

Finite Difference

Top Venues

J. Comput. Phys.

Appl. Math. Comput.

J. Sci. Comput.

Publications

Hong Zhang, Gengen Zhang, Ziyuan Liu, Xu Qian, Songhe Song
On the maximum principle and high-order, delay-free integrators for the viscous Cahn-Hilliard equation. Adv. Comput. Math. 50 (3) (2024)
Ziyuan Liu, Haifeng Wang, Hong Zhang, Kaijun Bao, Xu Qian, Songhe Song
Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Nonperiodic Boundary Conditions. SIAM J. Sci. Comput. 46 (4) (2024)
Jingwei Sun, Haifeng Wang, Hong Zhang, Xu Qian, Songhe Song
Global-in-time energy stability: a powerful analysis tool for the gradient flow problem without maximum principle or Lipschitz assumption. CoRR (2024)
Hong Zhang, Xu Qian, Songhe Song
Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation. Numer. Algorithms 95 (3) (2024)
Ziyuan Liu, Hong Zhang, Xu Qian, Songhe Song
Mass and energy conservative high-order diagonally implicit Runge-Kutta schemes for nonlinear Schrödinger equation. Appl. Math. Lett. 153 (2024)
Yan Wang, Xufeng Xiao, Hong Zhang, Xu Qian, Songhe Song
Efficient diffusion domain modeling and fast numerical methods for diblock copolymer melt in complex domains. Comput. Phys. Commun. 305 (2024)
Hong Zhang, Lele Liu, Xu Qian, Songhe Song
Large time-stepping, delay-free, and invariant-set-preserving integrators for the viscous Cahn-Hilliard-Oono equation. J. Comput. Phys. 499 (2024)
Lele Liu, Hong Zhang, Xu Qian, Songhe Song
High-order, large time-stepping integrators for scalar hyperbolic conservation laws. Commun. Nonlinear Sci. Numer. Simul. 131 (2024)
Haifeng Wang, Yabing Sun, Xu Qian, Songhe Song
A high-order compact difference scheme on graded mesh for time-fractional Burgers' equation. Comput. Appl. Math. 42 (1) (2023)
Ziyuan Liu, Yuhang Wu, Daniel Zhengyu Huang, Hong Zhang, Xu Qian, Songhe Song
SPFNO: Spectral operator learning for PDEs with Dirichlet and Neumann boundary conditions. CoRR (2023)
Jingwei Sun, Hong Zhang, Xu Qian, Songhe Song
Up to eighth-order maximum-principle-preserving methods for the Allen-Cahn equation. Numer. Algorithms 92 (2) (2023)
Jingwei Sun, Hong Zhang, Xu Qian, Songhe Song
A family of structure-preserving exponential time differencing Runge-Kutta schemes for the viscous Cahn-Hilliard equation. J. Comput. Phys. 492 (2023)
Tianchu Hao, Yaming Chen, Lingyan Tang, Songhe Song
A third-order weighted nonlinear scheme for hyperbolic conservation laws with inverse Lax-Wendroff boundary treatment. Appl. Math. Comput. 441 (2023)
Hong Zhang, Jingye Yan, Xu Qian, Xiaowei Chen, Songhe Song
Explicit Third-Order Unconditionally Structure-Preserving Schemes for Conservative Allen-Cahn Equations. J. Sci. Comput. 90 (1) (2022)
Chaolong Jiang, Jin Cui, Xu Qian, Songhe Song
High-Order Linearly Implicit Structure-Preserving Exponential Integrators for the Nonlinear Schrödinger Equation. J. Sci. Comput. 90 (1) (2022)
Xiaoqiang Yan, Xu Qian, Hong Zhang, Songhe Song
Numerical approximation to nonlinear delay-differential-algebraic equations with proportional delay using block boundary value methods. J. Comput. Appl. Math. 404 (2022)
Mingyang Cheng, Lingyan Tang, Yaming Chen, Songhe Song
A well-balanced weighted compact nonlinear scheme for shallow water equations on curvilinear grids. J. Comput. Phys. 463 (2022)
Chaolong Jiang, Xu Qian, Songhe Song, Chenxuan Zheng
Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation. CoRR (2022)
Ziyuan Liu, Haifeng Wang, Kaijun Bao, Xu Qian, Hong Zhang, Songhe Song
Render unto Numerics : Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions. CoRR (2022)
Xu Qian, Jian Dong, Songhe Song
Positivity-Preserving and Well-Balanced Adaptive Surface Reconstruction Schemes for Shallow Water Equations with Wet-Dry Fronts. J. Sci. Comput. 92 (3) (2022)
Kaijun Bao, Xu Qian, Ziyuan Liu, Haifeng Wang, Songhe Song
Function-valued RKHS-based Operator Learning for Differential Equations. CoRR (2022)
Hong Zhang, Jingye Yan, Xu Qian, Xiaowei Chen, Songhe Song
Correction to: Explicit Third-Order Unconditionally Structure-Preserving Schemes for Conservative Allen-Cahn Equations. J. Sci. Comput. 91 (1) (2022)
Chaolong Jiang, Jin Cui, Xu Qian, Songhe Song
High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation. CoRR (2021)
Hong Zhang, Jingye Yan, Xu Qian, Xianming Gu, Songhe Song
On the preserving of the maximum principle and energy stability of high-order implicit-explicit Runge-Kutta schemes for the space-fractional Allen-Cahn equation. Numer. Algorithms 88 (3) (2021)
Jingye Yan, Xu Qian, Hong Zhang, Songhe Song
Two regularized energy-preserving finite difference methods for the logarithmic Klein-Gordon equation. J. Comput. Appl. Math. 393 (2021)
Chaolong Jiang, Xu Qian, Songhe Song, Jin Cui
Arbitrary high-order linear structure-preserving schemes for the regularized long-wave equation. CoRR (2021)
Jingye Yan, Hong Zhang, Ziyuan Liu, Songhe Song
Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation. Appl. Math. Comput. 367 (2020)
Mingzhan Song, Xu Qian, Tianlong Shen, Songhe Song
Stochastic conformal schemes for damped stochastic Klein-Gordon equation with additive noise. J. Comput. Phys. 411 (2020)
Hong Zhang, Xu Qian, Songhe Song
Novel high-order energy-preserving diagonally implicit Runge-Kutta schemes for nonlinear Hamiltonian ODEs. Appl. Math. Lett. 102 (2020)
Hong Zhang, Xu Qian, Jingye Yan, Songhe Song
Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations. J. Comput. Phys. 418 (2020)
Ziyuan Liu, Hong Zhang, Xu Qian, Songhe Song
Mass and energy conservative high order diagonally implicit Runge-Kutta schemes for nonlinear Schrödinger equation in one and two dimensions. CoRR (2019)
Ziyuan Liu, Hong Zhang, Jingye Yan, Songhe Song
A fast mass-conserving explicit splitting method for the stochastic space-fractional nonlinear Schrödinger equation with multiplicative noise. Appl. Math. Lett. 98 (2019)
Jiarui Liang, Songhe Song, Weien Zhou, Hao Fu
Analysis of the damped nonlinear space-fractional Schrödinger equation. Appl. Math. Comput. 320 (2018)
Weien Zhou, Jingjing Zhang, Jialin Hong, Songhe Song
Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise. J. Comput. Appl. Math. 325 (2017)
Xu Qian, Hao Fu, Songhe Song
Conservative modified Crank-Nicolson and time-splitting wavelet methods for modeling Bose-Einstein condensates in delta potentials. Appl. Math. Comput. 307 (2017)
Xu Qian, Songhe Song, Yaming Chen
A semi-explicit multi-symplectic splitting scheme for a 3-coupled nonlinear Schrödinger equation. Comput. Phys. Commun. 185 (4) (2014)
Yaming Chen, Songhe Song, Huajun Zhu
Multi-symplectic methods for the Ito-type coupled KdV equation. Appl. Math. Comput. 218 (9) (2012)
Er Gao, Songhe Song, Xinjian Zhang
Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral. J. Appl. Math. 2012 (2012)
Huajun Zhu, Songhe Song, Yifa Tang
Multi-symplectic wavelet collocation method for the nonlinear Schrödinger equation and the Camassa-Holm equation. Comput. Phys. Commun. 182 (3) (2011)
Yaming Chen, Songhe Song, Huajun Zhu
The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs. J. Comput. Appl. Math. 236 (6) (2011)
Huajun Zhu, Lingyan Tang, Songhe Song, Yifa Tang, Desheng Wang
Symplectic wavelet collocation method for Hamiltonian wave equations. J. Comput. Phys. 229 (7) (2010)
Yaming Chen, Huajun Zhu, Songhe Song
Multi-symplectic splitting method for the coupled nonlinear Schrödinger equation. Comput. Phys. Commun. 181 (7) (2010)
Yu Wang, Songhe Song, Zhijun Tan, Desheng Wang
Adaptive variational curve smoothing based on level set method. J. Comput. Phys. 228 (17) (2009)
Songhe Song, Mao-Zhang Chen
Third Order Accurate Large-Particle Finite Volume Method on Unstructured Triangular Meshes. SIAM J. Sci. Comput. 23 (5) (2002)