代表性研究成果
(1) Guo S，Zhang Z, Mei L.Adaptive time-stepping Hermite spectral scheme for nonlinear Schrödinger equation with wave operator: Conservation of mass, energy, and momentum. Journal of Computational Physics,2025,528:113842.
(2)Zhang Z, Zhang Y, Guo S. Nesterov acceleration-based iterative method for backward problem of distributed-order time-fractional diffusion equation.
Mathematical Methods in the Applied Sciences, 2025, 48(2).
(3)Zhang Z, Guo S, Zhang Y. An iterative method based on Nesterov acceleration for identifying space-dependent source term in a time-fractional diffusion-wave equation. Journal of Computational and Applied Mathematics, 2023,429:115214.
(4)Zhang Z，Zhang Y. A fast iterative method for identifying the radiogenic source for the helium production-diffusion equation. Applied Mathematics in Science and Engineering, 2022(30).
(5)Yan X, Zhang Z, Wei T. Simultaneous inversion of a time-dependent potential coefficient and a time source term in a time fractional diffusion-wave equation. Chaos Solitons Fractals, 2022(157).
(6)Guo S, Mei L, Li C, Zhang Z, Li Y. Semi-implicit Hermite-Galerkin Spectral Method for Distributed-Order Fractional-in-Space Nonlinear Reaction-Diffusion Equations in Multidimensional Unbounded Domains. Journal of Scientific Computing, 2020, 85(15).
(7)Fu Z, Jin Q, Zhang Z, Han B, Chen Y. Analysis of a heuristic rule for the IRGNM in Banach spaces with convex regularization terms. Inverse Problems, 2020, 36(7): 075002.
(8)Guo S, Mei L, Zhang Z, et al.A linearized finite difference/spectral-Galerkin scheme for three-dimensional distributed-order time-space fractional nonlinear reaction-diffusion-wave equation: Numerical simulations of Gordon-type solitons, Computer Physics Communications,2020,252,107144.
(9)Li Y S, Sun L L, Zhang Z Q, Wei T. Identification of the time-dependent source term in a multi-term time-fractional diffusion equation. Numerical Algorithms, 2019, 82(4): 1279-1301.
(10)Guo S, Mei L, Hou Y, Zhang Z. An efficient finite difference/Hermite-Galerkin spectral method for time-fractional coupled sine-Gordon equations on multidimensional unbounded domains and its application in numerical simulations of vector solitons. Computer Physics Communications, 2019.
(11)Guo S, Mei L, Zhang Z, et al. Finite difference/Hermite-Galerkin spectral method for multi-dimensional time-fractional nonlinear reaction-diffusion equation in unbounded domains. Applied Mathematical Modelling, 2019, 70: 246-263.
(12)Zhang Z, Jin Q. Heuristic rule for non-stationary iterated Tikhonov regularization in Banach spaces. Inverse Problems, 2018, 34(11): 115002.
(13)Guo S, Mei L, Zhang Z, et al. Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time-space fractional reaction-diffusion equation. Applied Mathematics Letters, 2018, 85: 157-163.
(14)Wei T, Zhang Z Q. Robin coefficient identification for a time-fractional diffusion equation. Inverse Problems in Science and Engineering, 2016, 24(4): 647-666.
(15)Guo S, Mei L, Zhang Z. Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons. Physics of Plasmas, 2015, 22(5).
(16)Wei T, Zhang Z Q. Stable numerical solution to a Cauchy problem for a time fractional diffusion equation. Engineering Analysis with Boundary Elements, 2014, 40: 128-137.
(17)Zhang Z Q, Ma Y J. A modified kernel method for numerical analytic continuation. Inverse Problems in Science and Engineering, 2013, 21(5): 840-853.
(18)Zhang Z Q, Wei T. An optimal regularization method for space-fractional backward diffusion problem. Mathematics and Computers in Simulation, 2013, 92: 14-27.
(19)Zhang Z Q, Wei T. Identifying an unknown source in time-fractional diffusion equation by a truncation method. Applied Mathematics and Computation, 2013, 219(11): 5972-5983.
(20)Wei T, Zhang Z Q. Reconstruction of a time-dependent source term in a time-fractional diffusion equation. Engineering Analysis with Boundary Elements, 2013, 37(1): 23-31.
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