个人简历

2018年1月- 南京航空航天大学理学院
研究方向：
计算数学
自适应算法、偏微分-积分方程数值解
承担的科研项目情况：
2018年1月-2020年12月 新教师启动基金项目
2021年1月-2024年12月 国家基金委面上项目(批准号：12071216)
教育经历
2005.9-2010.9 东南大学 | 应用数学 | 理学博士学位 | 博士研究生毕业
1998.9-2001.6 解放军理工大学 | 应用数学 | 理学硕士学位 | 硕士研究生毕业
1994.9-1998.7 原空军气象学院 | 大气科学 | 理学学士学位 | 大学本科毕业
工作经历
2017.7-2017.12 陆军工程大学
2001.6-2017.6 解放军理工大学
科研项目当
[1]廖洪林科研启动经费
[2]分数阶扩散方程的非均匀离散与数值分析
[3]分数阶扩散方程的非均匀离散与数值分析
[4]分数阶扩散方程的非均匀离散与数值分析
授课信息：
数学建模 /2020-2021 /春学期 /32课时 /0.0学分 /081X0030.02
数学建模 /2020-2021 /春学期 /32课时 /0.0学分 /081X0030.01

研究领域

分数阶微分方程数值解
偏微分方程数值解""

近期论文

[19] Hong-lin Liao, Tao Tang and Tao Zhou, Positive definiteness of real quadratic forms resulting from variable-step approximations of convolution operators, 2020, arXiv:2011.13383v1.
[18] Hong-lin Liao, Tao Tang and Tao Zhou, An energy stable and maximum bound preserving scheme with variable time steps for time fractional Allen-Cahn equation, SIAM Journal on Scientific Computing, 2021, 43(5): A3503-B3526.
[17] Hong-lin Liao, William McLean and Jiwei Zhang, A second-order scheme with nonuniform time steps for a linear reaction-subdiffusion problem, Communications in Computational Physics, 2021, 30(2)：567-601, doi:10.4208/cicp.OA-2020-0124.
[16] Jincheng Ren, Hong-lin Liao (corresponding), Jiwei Zhang and Zhimin Zhang, Sharp H1-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems, Journal of Computational and Applied Mathematics, 389 (2021), 113352, doi: 10.1016/j.cam.2020.113352.
[15] Hong-lin Liao, Xuehua Song, Tao Tang and Tao Zhou, Analysis of the second order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection, Science China Mathematics, 64 (2021), 887-902, doi:10.1007/s11425-020-1817-4.
[14] Hong-lin Liao, Bingquan Ji and Luming Zhang, An adaptive BDF2 implicit time-stepping method for the phase field crystal model, IMA Journal on Numerical Analysis, 41 (2021), doi:10.1093/imanum/draa075.
[13] Hong-lin Liao and Zhimin Zhang, Analysis of adaptive BDF2 scheme for diffusion equations, Mathematics of Computation, 90 (2021), 1207-1226, DOI: 10.1090/mcom/3585.
[12] Jincheng Ren, Hong-lin Liao (corresponding) and Zhimin Zhang, Superconvergence error estimate of a finite element method on nonuniform time meshes for reaction-subdiffusion equations, Journal of Scientific Computing, 84 (2020), 38, DOI: 10.1007/s10915-020-01290-1.
[11] Hong-lin Liao, Tao Tang and Tao Zhou, A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations, Journal of Computational Physics, 414 (2020), 109473 , DOI: 10.1016/j.jcp.2020.109473.
[10] Bingquan Ji, Hong-lin Liao (corresponding) and Luming Zhang, Simple maximum- principle preserving time-stepping methods for time-fractional Allen-Cahn equation, Advances in Computational Mathematics, 46(2), 2020, 37, DOI: 10.1007/s10444-020-09782-2.
[9] Hong-lin Liao, Tao Tang and Tao Zhou, On energy stable, maximum bound preserving, second order BDF scheme with variable steps for the Allen-Cahn equation, SIAM Journal on Numerical Analysis, 2020, 58(4): 2294-2314.
[8] Bingquan Ji, Hong-lin Liao(corresponding), Yuezheng Gong and Luming Zhang, Adaptive second-order Crank-Nicolson time-stepping schemes for time fractional molecular beam epitaxial growth models, SIAM Journal on Scientific Computing，2020, 42(3): B738-B760.
[7] Hong-lin Liao, William McLean and Jiwei Zhang, A discrete Gronwall inequality with applications to numerical schemes for subdiffusion problems, SIAM Journal on Numerical Analysis, 57(1) (2019), 218-237.
[6] Hong-lin Liao, Dongfang Li and Jiwei Zhang, Sharp error estimate of nonuniform L1 formula for time-fractional reaction-subdiffusion equations, SIAM Journal on Numerical Analysis, 56(2) (2018), 1112-1133.
[5] Ya-nan Zhang, Zhi-zhong Sun and Hong-lin Liao, Finite difference methods for the time fractional diffusion equation on non-uniform meshes, Journal of Computational Physics, 265 (2014), 195-210.
[4] 廖洪林, 孙志忠, 史汉生, 二维非线性Schrodinger 方程显式格式的最大模误差分析, 中国科学A辑：数学, 40(9) (2010), 827-842.
[3] Hong-lin Liao, Zhi-zhong Sun and Han-sheng Shi, Error estimate of fourth-order compact scheme for solving linear Schrodinger equations, SIAM Journal on Numerical Analysis, 47(6) (2010), 4381-4401.
[2] Hong-lin Liao, Han-sheng Shi and Zhi-zhong Sun, Corrected explicit-implicit domain decomposition algorithms for two-dimensional semilinear parabolic equations, Science in China Series A-Mathematics, 52(11) (2009), 2362-2388.
(中文版) 廖洪林, 史汉生, 孙志忠, 求解二维半线性抛物方程的校正型显隐区域分解算法, 中国科学A辑-数学, 39(6) (2009), 749-774.
[1] Han-sheng Shi, Hong-lin Liao (corresponding), Unconditional stability of corrected explicit-implicit domain decomposition algorithms for parallel approximation of heat equations, SIAM Journal on Numerical Analysis, 44(4) (2006), 1584-1611.
1] 纪兵权,廖洪林,龚跃政等.Adaptive second-order Crank-Nicolson time-stepping schemes for time-fractional molecular beam epitaxial growth models[J].SIAM J. Sci. Comput.,2020,3(42):B738-B760
[2] 纪兵权,廖洪林,龚跃政等.Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint[J].Commun. Nonlinear Sci. Numer. Simul.,2020(90):105366
[3] 廖洪林,,等.A DISCRETE GRONWALL INEQUALITY WITH APPLICATIONS TO NUMERICAL SCHEMES FOR SUBDIFFUSION PROBLEMS.SIAM JOURNAL ON NUMERICAL ANALYSIS,2019
[4] 廖洪林,,等.Unconditional Convergence of a Fast Two-Level Linearized Algorithm for Semilinear Subdiffusion Equations.J Sci Comput,2019