Latest Update: Dec 2024

Submitted Paper

• 5.  A meshless energy-preserving scheme for conservative partial differential equations using kernel-based Galerkin methods
  Zhongting Xu, Zhengjie Sun*, Shengliang Zhang-submitted, 2024

• 4.  A meshless structure-preserving quasi-interpolation method for the Allen-Cahn equation on spheres
  Zhengjie Sun*-submitted, 2024

• 3.  High-order quasi-interpolation with generalized Gaussian kernels restricted over tori (arXiv:2407.21283)
  Wenwu Gao, Zhengjie Sun*, Changwei Wang-submitted, 2024

• 2.  Spherical quasi-interpolation using scaled zonal kernels (arXiv:2408.14803)
  Zhengjie Sun, Wenwu Gao, Xingping Sun-submitted, 2024

• 1.  Energy-conserving Kansa methods for Hamiltonian wave equations
  Xiaobin Li, Meng Chen, Zhengjie Sun, Leevan Ling, Siqing Li-submitted, 2024

  
  

Journal Paper

• 22.  Learning PDEs from data on closed surfaces with sparse optimization
  Zhengjie Sun, Leevan Ling, Ran Zhang*
  Communications in Computational Physics, 37:289-314, 2025 (arXiv:2405.06199)

• 21.  Energy-equidistributed moving mesh strategies for simulating Hamiltonian partial differential equations
  Qinjiao Gao, Zhengjie Sun*, Zongmin Wu
  Applied mathematics letters, 163, 109460, 2025.

• 20.  Structure-preserving kernel-based methods for solving dissipative PDEs on surfaces
  Zhengjie Sun, Leevan Ling, and Meng Chen
  Journal of Scientific Computing, 102(3):70, 2025. (arXiv:2312.17478)

• 19.  Quasi-interpolation for high-dimensional function approximation
  Wenwu Gao, Jiecheng Wang, Zhengjie Sun*, Gregory E. Fasshauer
  Numerische Mathematik, 156:1855–1885, 2024 (arXiv:2409.14278)

• 18.  A high-order meshless linearly implicit energy-preserving method for nonlinear wave equations on Riemannian manifolds
  Zhengjie Sun*, Leevan Ling
  SIAM Journal on Scientific Computing, 46(6):A3779-3802, 2024

• 17.  Energy-preserving schemes for conservative PDEs based on periodic quasi-interpolation methods
  Zhengjie Sun, Qinjiao Gao*
  Communications in Nonlinear Science and Numerical Simulation, 131, 107831, 2024

• 16.  High order multiquadric trigonometric quasi-interpolation method for solving time-dependent partial differential equations
  Zhengjie Sun, Yuyan Gao*
  Numerical Algorithms, 93:1719-1739, 2023

• 15.  A radial basis function approximation method for conservative Allen-Cahn equations on surfaces
  Zhengjie Sun, Shengliang Zhang*
  Applied Mathematics Letters, 143:108634, 2023

• 14.  Meshless symplectic and multi-symplectic scheme for the coupled nonlinear Schrödinger system based on local RBF approximation
  Shengliang Zhang, Zhengjie Sun*, Alpesh Kumar
  Computers & Mathematics with Applications, 134:16-32, 2023

• 13.  A meshless quasi-interpolation method for solving hyperbolic conservation laws based on the essentially non-oscillatory reconstruction
  Zhengjie Sun*, Yuyan Gao
  International Journal of Computer Mathematics, 100(6):1303-1320, 2023

• 12.  A kernel-based meshless conservative Galerkin method for solving Hamiltonian wave equations
  Zhengjie Sun, Leevan Ling*
  SIAM Journal on Scientific Computing, 44(4):A2789-2807, 2022

• 11.  A convergent iterated quasi-interpolation for periodic domain and its applications to surface PDEs
  Zhengjie Sun, Wenwu Gao, Ran Yang*
  Journal of Scientific Computing, 93(2):37, 2022

• 10.  A conservative scheme for two-dimensional Schrödinger equation based on multi-quadric trigonometric quasi-interpolation approach
  Zhengjie Sun*
  Applied Mathematics and Computation, 423, 2022, 12pp

• 9.  Multi-symplectic quasi-interpolation method for the KdV equation
  Yuyan Gao, Zhengjie Sun*
  Computational and Applied Mathematics, 41(3):112, 17pp, 2022

• 8.  An iterated quasi-interpolation approach for derivative approximation
  Zhengjie Sun, Zongmin Wu, Wenwu Gao*
  Numerical Algorithms, 85:255-276, 2020

• 7.  Multi-symplectic quasi-interpolation method for Hamiltonian partial differential equations
  Zhengjie Sun*
  Journal of Computational Physics, 395:125-143, 2019

• 6.  High-order numerical solution of time-dependent differential equations with quasi-interpolation
  Wenwu Gao, Zhengjie Sun*
  Applied Numerical Mathematics, 146:276-290, 2019

• 5.  A meshless symplectic method for two-dimensional nonlinear Schrödinger equations based on radial basis function approximation
  Zhengjie Sun*
  Engineering Analysis with Boundary Elements, 104:1-7, 2019

• 4.  Meshless conservative schemes for multivariate Hamiltonian partial differential equations
  Zhengjie Sun, Zongmin Wu*
  Journal of Scientific Computing, 76:1168-1187, 2018

• 3.  A energy-momentum conserving scheme for Hamiltonian wave equation based on multiquadric trigonometric quasi-interpolation
  Zhengjie Sun, Wenwu Gao*
  Applied Mathematical Modelling, 57:179-191, 2018

• 2.  Conservative or dissipative quasi-interpolation method for evolutionary partial differential equations
  Zhengjie Sun*
  Engineering Analysis with Boundary Elements, 96:78-83, 2018

• 1.  A meshless scheme for Hamiltonian partial differential equations with conservation properties
  Zhengjie Sun, Wenwu Gao*
  Applied Numerical Mathematics, 119:115-125, 2017