刘凯 中共党员
最后学位: 博士
岗位职称：副教授
研究领域：微分方程保结构数值算法
教学课程：微积分、线性代数、概率论、矩阵论
办公室：位育楼307
Email ：laukai520@163.com
通讯地址：南京市浦口区雨山西路86号
邮 编：211815
学习经历
2004.09-2008.06 中国石油大学(华东) 数学与应用数学 理学学士
2008.09-2011.06 中国石油大学(华东) 应用数学 理学硕士
2011.09-2015.06 南京大学 计算数学 理学博士
2014.02-2015.02 剑桥大学 计算数学 联合培养
工作经历
2015.06-2019.05 南京财经大学应用数学学院 讲师
2019.06-2021.08 南京财经大学应用数学学院 副教授
2021.09—至今 南京审计大学数学学院 副教授
主持课题
1.国家自然科学基金青年项目：几类微分方程的保结构算法研究， 项目编号：11701271， 2018.01-2020.12.
2.江苏省高校自然科学研究面上项目: 二阶振荡微分方程保结构算法研究，项目编号：16KJB110010, 2016.01-2018.12
代表性期刊论文
（1） Kai Liu, Bin Wang and Ting Fu, Relaxation RKN-type integrators that preserve two invariants for second-order (oscillatory) systems, Journal of Computational and Applied Mathematics, 457, 116300, 2025.
（2） Kai Liu, Bin Wang and Xiaofei Zhao, SOLVING THE LONG-TIME NONLINEAR SCHRÖDINGER EQUATION BY A CLASS OF OSCILLATION-RELAXATION INTEGRATORS, Multiscale Modeling and Simulation, 23(1), 313-338, 2025.
（3） Kai Liu, Ting Fu, Linearly-fitted energy-mass-preserving schemes for Korteweg-de Vries equations, Journal of Computational and Applied Mathematics, 448, 115914, 2024.
（4） Kai Liu, Ting Fu, Wei Shi and Xuhuan Zhou, A new type of energy-preserving integrators for quasi-bi-Hamiltonian systems, Journal of Mathematical Chemistry, 62(7), 1667-1681, 2024.
（5） Kai Liu, Mingqian Zhang and Xiong You, A variant of the discrete gradient method for the solution of the semilinear wave equation under different boundary conditions, Computers and Mathematics with Applications, 158, 199-218, 2024.
（6） Changying Liu, Kai Liu(通讯作者), A fourth-order energy-preserving and symmetric average vector field integrator with low regularity assumption, Journal of Computational and Applied Mathematics, 439, 115605, 2024.
（7） Changying Liu, Jiayin Li, Zhenqi Yang, Yumeng Tang and Kai Liu(通讯作者), Two high-order energy-preserving and symmetric Gauss collocation integrators for solving the hyperbolic Hamiltonian systems, Mathematics and Computers in Simulation, 205, 19-32, 2023.
（8） Wei Shi, Kai Liu(通讯作者), A DISSIPATION-PRESERVING INTEGRATOR FOR DAMPED OSCILLATORY HAMILTONIAN SYSTEMS, Journal of Computational Mathematics, 40 (4), 573-591,2022.
（9） Kai Liu, Mingqian Zhang , Wei Shi and Jie Yang, A new Jacobi-type iteration method for solving M-matrix or nonnegative linear systems, Japan Journal of Industrial and Applied Mathematics, 39(1), 403-417, 2022.
（10） Kai Liu, Ting Fu and Wei Shi, Stability Analysis for Explicit ERKN Methods Solving General Second-Order Oscillatory Systems, Bulletin of the Malaysian Mathematical Sciences Society, 44, 4143-4154, 2021.
（11） Kai Liu, Ting Fu and Wei Shi, A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting, Applied Numerical Mathematics, 170, 242-254, 2021.
（12） Ting Fu, Mingqian Zhang and Kai Liu(通讯作者), An integral evolution formula of boundary value problem for wave equations, Applied Mathematics Letters, 116, 107066, 2020.
（13） Wei Shi, Xinyuan Wu and Kai Liu(通讯作者), Efficient implementation of the ARKN and ERKN integrators for multi-frequency oscillatory systems with multiple time scales, Applied Numerical Mathematics, 151, 13-26, 2020.
（14） Kai Liu, Jie Yang and Wei Shi, A new SOR-type iteration method for solving linear systems, Applied Mathematics Letters, 102, 106104, 2020.
（15） Kai Liu, Jie Yang and Changying Liu, A new iterative refinement for ill-conditioned linear systems based on discrete gradient, Japan Journal of Industrial and Applied Mathematics, 37, 803-818, 2020.
（16） Wei Shi, Kai Liu(通讯作者), Periodic solutions to nonlinear wave equations with x-dependent coefficients at resonance, Rocky Mountain Journal of Mathematics, 48, 1291-1306, 2018.
（17） Wei Shi, Kai Liu(通讯作者), A new analytical formula for the wave equations with variable coefficients, Applied Mathematics Letters, 84, 137-142, 2018.
（18） Kai Liu, Wei Shi, High-order skew-symmetric differentiation matrix on symmetric grid, Journal of Computational and Applied Mathematics, 343, 206-216, 2018.
（19） Kai Liu, Wei Shi, The Cauchy problem for linear inhomogeneous wave equations with variable coefficients. Applied Mathematics Letters, 86, 215-221, 2018.
（20） Kai Liu, Xinyuan Wu and Wei Shi, Extended phase properties and stability analysis of RKN-type integrators for solving general oscillatory second-order initial value problems, Numerical Algorithms, 77, 37-56, 2018.
（21） Kai Liu, A Linearly-Fitted Conservative (Dissipative) Scheme for Efficiently Solving Conservative (Dissipative) Nonlinear Wave PDEs, Journal of Computational Mathematics, 35, 780-800, 2017.
（22） Kai Liu, Xinyuan Wu, High-Order Symplectic and Symmetric Composition Methods for Multi-Frequency and Multi-Dimensional Oscillatory Hamiltonian Systems. Journal of Computational Mathematics, 33, 356-378, 2015.
（23） Kai Liu, Xinyuan Wu, Multidimensional ARKN methods for general oscillatory second-order initial value problems, Computer Physics Communications, 185, 1999-2007, 2014.
（24） Kai Liu, Wei Shi and Xinyuan Wu, An extended discrete gradient formula for oscillatory Hamiltonian systems, Journal of Physics A: Mathematical and Theoretical, 46, 165203, 2013.