Third Order Accurate Large-Particle Finite Volume Method on Unstructured Triangular Meshes. - Songhe Song; Mao-Zhang Chen (SIAM J. Sci. Comput., 2002)

Adaptive variational curve smoothing based on level set method. - Yu Wang 029; Songhe Song; Zhijun Tan; Desheng Wang (J. Comput. Phys., 2009)

Multi-symplectic splitting method for the coupled nonlinear Schrödinger equation. - Yaming Chen; Huajun Zhu; Songhe Song (Comput. Phys. Commun., 2010)

Symplectic wavelet collocation method for Hamiltonian wave equations. - Huajun Zhu; Lingyan Tang; Songhe Song; Yifa Tang; Desheng Wang (J. Comput. Phys., 2010)

Multi-symplectic wavelet collocation method for the nonlinear Schrödinger equation and the Camassa-Holm equation. - Huajun Zhu; Songhe Song; Yifa Tang (Comput. Phys. Commun., 2011)

The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs. - Yaming Chen; Songhe Song; Huajun Zhu (J. Comput. Appl. Math., 2011)

Multi-symplectic methods for the Ito-type coupled KdV equation. - Yaming Chen; Songhe Song; Huajun Zhu (Appl. Math. Comput., 2012)

Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral. - Er Gao; Songhe Song; Xinjian Zhang (J. Appl. Math., 2012)

A semi-explicit multi-symplectic splitting scheme for a 3-coupled nonlinear Schrödinger equation. - Xu Qian; Songhe Song; Yaming Chen (Comput. Phys. Commun., 2014)

Conservative modified Crank-Nicolson and time-splitting wavelet methods for modeling Bose-Einstein condensates in delta potentials. - Xu Qian; Hao Fu 001; Songhe Song (Appl. Math. Comput., 2017)

Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise. - Weien Zhou; Jingjing Zhang 003; Jialin Hong; Songhe Song (J. Comput. Appl. Math., 2017)

Analysis of the damped nonlinear space-fractional Schrödinger equation. - Jiarui Liang; Songhe Song; Weien Zhou; Hao Fu 001 (Appl. Math. Comput., 2018)

A fast mass-conserving explicit splitting method for the stochastic space-fractional nonlinear Schrödinger equation with multiplicative noise. - Ziyuan Liu; Hong Zhang 008; Jingye Yan; Songhe Song (Appl. Math. Lett., 2019)

Mass and energy conservative high order diagonally implicit Runge-Kutta schemes for nonlinear Schrödinger equation in one and two dimensions. - Ziyuan Liu; Hong Zhang 008; Xu Qian; Songhe Song (CoRR, 2019)

Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation. - Jingye Yan; Hong Zhang 008; Ziyuan Liu; Songhe Song (Appl. Math. Comput., 2020)

Novel high-order energy-preserving diagonally implicit Runge-Kutta schemes for nonlinear Hamiltonian ODEs. - Hong Zhang 008; Xu Qian; Songhe Song (Appl. Math. Lett., 2020)

Stochastic conformal schemes for damped stochastic Klein-Gordon equation with additive noise. - Mingzhan Song; Xu Qian; Tianlong Shen; Songhe Song (J. Comput. Phys., 2020)

Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations. - Hong Zhang 008; Xu Qian; Jingye Yan; Songhe Song (J. Comput. Phys., 2020)

Arbitrary high-order linear structure-preserving schemes for the regularized long-wave equation. - Chaolong Jiang; Xu Qian; Songhe Song; Jin Cui (CoRR, 2021)

Two regularized energy-preserving finite difference methods for the logarithmic Klein-Gordon equation. - Jingye Yan; Xu Qian; Hong Zhang 008; Songhe Song (J. Comput. Appl. Math., 2021)

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. - Hong Zhang 008; Jingye Yan; Xu Qian; Xianming Gu; Songhe Song (Numer. Algorithms, 2021)

Function-valued RKHS-based Operator Learning for Differential Equations. - Kaijun Bao; Xu Qian; Ziyuan Liu; Haifeng Wang; Songhe Song (CoRR, 2022)

Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation. - Chaolong Jiang; Xu Qian; Songhe Song; Chenxuan Zheng (CoRR, 2022)

Render unto Numerics : Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions. - Ziyuan Liu; Haifeng Wang; Kaijun Bao; Xu Qian; Hong Zhang 008; Songhe Song (CoRR, 2022)

Numerical approximation to nonlinear delay-differential-algebraic equations with proportional delay using block boundary value methods. - Xiaoqiang Yan; Xu Qian; Hong Zhang 008; Songhe Song (J. Comput. Appl. Math., 2022)

A well-balanced weighted compact nonlinear scheme for shallow water equations on curvilinear grids. - Mingyang Cheng; Lingyan Tang; Yaming Chen; Songhe Song (J. Comput. Phys., 2022)

High-Order Linearly Implicit Structure-Preserving Exponential Integrators for the Nonlinear Schrödinger Equation. - Chaolong Jiang; Jin Cui; Xu Qian; Songhe Song (J. Sci. Comput., 2022)

Positivity-Preserving and Well-Balanced Adaptive Surface Reconstruction Schemes for Shallow Water Equations with Wet-Dry Fronts. - Xu Qian; Jian Dong; Songhe Song (J. Sci. Comput., 2022)

Explicit Third-Order Unconditionally Structure-Preserving Schemes for Conservative Allen-Cahn Equations. - Hong Zhang 008; Jingye Yan; Xu Qian; Xiaowei Chen; Songhe Song (J. Sci. Comput., 2022)

Correction to: Explicit Third-Order Unconditionally Structure-Preserving Schemes for Conservative Allen-Cahn Equations. - Hong Zhang 008; Jingye Yan; Xu Qian; Xiaowei Chen; Songhe Song (J. Sci. Comput., 2022)

A third-order weighted nonlinear scheme for hyperbolic conservation laws with inverse Lax-Wendroff boundary treatment. - Tianchu Hao; Yaming Chen; Lingyan Tang; Songhe Song (Appl. Math. Comput., 2023)

SPFNO: Spectral operator learning for PDEs with Dirichlet and Neumann boundary conditions. - Ziyuan Liu; Yuhang Wu; Daniel Zhengyu Huang; Hong Zhang; Xu Qian; Songhe Song (CoRR, 2023)

Up to eighth-order maximum-principle-preserving methods for the Allen-Cahn equation. - Jingwei Sun; Hong Zhang 008; Xu Qian; Songhe Song (Numer. Algorithms, 2023)

A high-order compact difference scheme on graded mesh for time-fractional Burgers' equation. - Haifeng Wang; Yabing Sun; Xu Qian; Songhe Song (Comput. Appl. Math., 2023)

A family of structure-preserving exponential time differencing Runge-Kutta schemes for the viscous Cahn-Hilliard equation. - Jingwei Sun; Hong Zhang 008; Xu Qian; Songhe Song (J. Comput. Phys., 2023)

Mass and energy conservative high-order diagonally implicit Runge-Kutta schemes for nonlinear Schrödinger equation. - Ziyuan Liu; Hong Zhang 008; Xu Qian; Songhe Song (Appl. Math. Lett., 2024)

Global-in-time energy stability: a powerful analysis tool for the gradient flow problem without maximum principle or Lipschitz assumption. - Jingwei Sun; Haifeng Wang; Hong Zhang; Xu Qian; Songhe Song (CoRR, 2024)

An exponential-free Runge-Kutta framework for developing third-order unconditionally energy stable schemes for the Cahn-Hilliard equation. - Haifeng Wang; Jingwei Sun; Hong Zhang; Xu Qian; Songhe Song (CoRR, 2024)

Efficient diffusion domain modeling and fast numerical methods for diblock copolymer melt in complex domains. - Yan Wang; Xufeng Xiao; Hong Zhang 008; Xu Qian; Songhe Song (Comput. Phys. Commun., 2024)

Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Nonperiodic Boundary Conditions. - Ziyuan Liu; Haifeng Wang; Hong Zhang 008; Kaijun Bao; Xu Qian; Songhe Song (SIAM J. Sci. Comput., 2024)

Large time-stepping, delay-free, and invariant-set-preserving integrators for the viscous Cahn-Hilliard-Oono equation. - Hong Zhang 008; Lele Liu; Xu Qian; Songhe Song (J. Comput. Phys., 2024)

Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation. - Hong Zhang 008; Xu Qian; Songhe Song (Numer. Algorithms, 2024)

High-order, large time-stepping integrators for scalar hyperbolic conservation laws. - Lele Liu; Hong Zhang 008; Xu Qian; Songhe Song (Commun. Nonlinear Sci. Numer. Simul., 2024)

On the maximum principle and high-order, delay-free integrators for the viscous Cahn-Hilliard equation. - Hong Zhang 008; Gengen Zhang; Ziyuan Liu; Xu Qian; Songhe Song (Adv. Comput. Math., 2024)

A nonlinear immersed boundary method for weighted compact nonlinear schemes. - Tianchu Hao; Yaming Chen; Lingyan Tang; Songhe Song (Appl. Math. Comput., 2025)

High-order Runge-Kutta type large time-stepping schemes for the compressible Euler equations. - Lele Liu; Songhe Song (Appl. Math. Lett., 2025)

Linearly implicit and large time-stepping conservative exponential relaxation schemes for the nonlocal cubic Gross-Pitaevskii equation. - Yayun Fu; Xu Qian; Songhe Song; Dongdong Hu (Adv. Comput. Math., 2025)

On the Convergence and Energy Stability Analysis for a Second-Order Scheme of the Swift-Hohenberg Equation. - Jingwei Sun; Haifeng Wang; Hong Zhang 008; Xu Qian; Songhe Song (J. Sci. Comput., 2025)

High-order energy-preserving methods for the coupled Klein-Gordon-Schrödinger equations with fractional Laplacian. - Yulian Yi; Mingfa Fei; Hong Zhang; Songhe Song (Comput. Appl. Math., 2025)