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Latest Update: Oct 2025

Preprints

  •  Zhengjie Sun*, Mengyuan Lv and Xingping Sun. Monte Carlo quasi-interpolation of spherical data, submitted, 2025. (arXiv:2510.12027)
  •  Zhengjie Sun* and Leevan Ling. Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds, submitted, 2025. (arXiv:2508.05376)
  •  Zhongting Xu, Zhengjie Sun* and Shengliang Zhang. A meshless energy-preserving scheme for conservative partial differential equations using kernel-based Galerkin methods, submitted, 2024.
  •  Wenwu Gao, Le Hu, Zhengjie Sun* and Changwei Wang. Quasi-interpolation using generalized Gaussian kernels, submitted, 2025. (arXiv:2407.21283)

Published papers

  •  Zhengjie Sun and Yuyan Gao*. A meshless structure-preserving quasi-interpolation method for the Allen-Cahn equation on spheres, Mathematics and Computers in Simulation, 241, 31-47, 2026.
  •  Zhengjie Sun, Wenwu Gao* and Xingping Sun. Scaled zonal kernel quasi-interpolation on spheres, IMA Journal of Numerical Analysis, doi.org/10.1093/imanum/draf104, 2025. (arXiv:2408.14803)
  •  Zhengjie Sun, Leevan Ling and Ran Zhang*. Learning PDEs from data on closed surfaces with sparse optimization, Communications in Computational Physics, 37:289-314, 2025. (arXiv:2405.06199)
  •  Qinjiao Gao, Zhengjie Sun* and Zongmin Wu. Energy-equidistributed moving mesh strategies for simulating Hamiltonian partial differential equations, Applied Mathematics Letters, 163, 109460, 2025.
  •  Zhengjie Sun*, Leevan Ling and Meng Chen. Structure-preserving kernel-based methods for solving dissipative PDEs on surfaces, Journal of Scientific Computing, 102(3):70, 2025. (arXiv:2312.17478)
  •  Wenwu Gao, Jiecheng Wang, Zhengjie Sun* and Gregory E. Fasshauer. Quasi-interpolation for high-dimensional function approximation, Numerische Mathematik, 156:1855–1885, 2024. (arXiv:2409.14278)
  •  Zhengjie Sun* and Leevan Ling. A high-order meshless linearly implicit energy-preserving method for nonlinear wave equations on Riemannian manifolds, SIAM Journal on Scientific Computing, 46(6):A3779-3802, 2024.
  •  Zhengjie Sun and Qinjiao Gao*. Energy-preserving schemes for conservative PDEs based on periodic quasi-interpolation methods, Communications in Nonlinear Science and Numerical Simulation, 131, 107831, 2024.
  •  Zhengjie Sun* and Yuyan Gao. High order multiquadric trigonometric quasi-interpolation method for solving time-dependent partial differential equations, Numerical Algorithms, 93:1719-1739, 2023.
  •  Zhengjie Sun and Shengliang Zhang*. A radial basis function approximation method for conservative Allen-Cahn equations on surfaces, Applied Mathematics Letters, 143, 108634, 2023.
  •  Shengliang Zhang, Zhengjie Sun* and Alpesh Kumar. Meshless symplectic and multi-symplectic scheme for the coupled nonlinear Schrödinger system based on local RBF approximation, Computers & Mathematics with Applications, 134:16-32, 2023.
  •  Zhengjie Sun* and Yuyan Gao. A meshless quasi-interpolation method for solving hyperbolic conservation laws based on the essentially non-oscillatory reconstruction, International Journal of Computer Mathematics, 100(6):1303-1320, 2023.
  •  Zhengjie Sun and Leevan Ling*. A kernel-based meshless conservative Galerkin method for solving Hamiltonian wave equations, SIAM Journal on Scientific Computing, 44(4):A2789-2807, 2022.
  •  Zhengjie Sun, Wenwu Gao and Ran Yang*. A convergent iterated quasi-interpolation for periodic domain and its applications to surface PDEs, Journal of Scientific Computing, 93(2):37, 2022.
  •  Zhengjie Sun*. A conservative scheme for two-dimensional Schrödinger equation based on multi-quadric trigonometric quasi-interpolation approach, Applied Mathematics and Computation, 423, 2022, 12pp.
  •  Yuyan Gao and Zhengjie Sun*. Multi-symplectic quasi-interpolation method for the KdV equation, Computational and Applied Mathematics, 41(3):112, 17pp, 2022.
  •  Zhengjie Sun, Zongmin Wu and Wenwu Gao*. An iterated quasi-interpolation approach for derivative approximation, Numerical Algorithms, 85:255-276, 2020.
  •  Zhengjie Sun*. Multi-symplectic quasi-interpolation method for Hamiltonian partial differential equations, Journal of Computational Physics, 395:125-143, 2019.
  •  Wenwu Gao and Zhengjie Sun*. High-order numerical solution of time-dependent differential equations with quasi-interpolation, Applied Numerical Mathematics, 146:276-290, 2019.
  •  Zhengjie Sun*. A meshless symplectic method for two-dimensional nonlinear Schrödinger equations based on radial basis function approximation, Engineering Analysis with Boundary Elements, 104:1-7, 2019.
  •  Zhengjie Sun and Zongmin Wu*. Meshless conservative schemes for multivariate Hamiltonian partial differential equations, Journal of Scientific Computing, 76:1168-1187, 2018.
  •  Zhengjie Sun and Wenwu Gao*. A energy-momentum conserving scheme for Hamiltonian wave equation based on multiquadric trigonometric quasi-interpolation, Applied Mathematical Modelling, 57:179-191, 2018.
  •  Zhengjie Sun*. Conservative or dissipative quasi-interpolation method for evolutionary partial differential equations, Engineering Analysis with Boundary Elements, 96:78-83, 2018.
  •  Zhengjie Sun and Wenwu Gao*. A meshless scheme for Hamiltonian partial differential equations with conservation properties, Applied Numerical Mathematics, 119:115-125, 2017.