姓名： 乔雷洁，女，博士，副教授。主要研究方向：偏微分方程数值解；机器学习方法求解偏微分方程。

电子邮箱：qiaoleijie@yeah.net

通信地址：山西省太原市小店区坞城路92号山西大学

教育经历

2013.09-2018.07 湖南师范大学 J9国际集团 计算数学 硕博连读

论文题目：分数次偏积分微分方程配置方法及紧差分方法

该论文主要采用紧差分方法研究二维分数次卷积方程，采用三次正交样条方法研究二维时间分数阶扩散方程。主要内容发表在International Journal of Computer Mathematics和Journal of scientific computing。

工作经历

2022.5-至今        山西大学 J9国际集团 副教授

2021.07-2022.12              北京大学 数学科学学院 计算数学 访问学者 胡俊 教授

2019.12-2020.09              英国切斯特大学 数学与工程学院 计算数学 访问学者 闫玉斌 教授

2018.07-2020.07              广东工业大学 应用数学学院 计算数学 博士后

科研项目

2025.01-2028.12	三晋英才项目	项目负责人（乔雷洁）
2024.01-2026.12	山西大学文瀛青年学者项目	项目负责人（乔雷洁）
2024.12-2026.12	深度学习与传染病传播动力学模型的融合理论与机理推断研究（重大研究计划培育项目）	项目参与者
2024.12-2025.5	基于机器学习与数值优化的农业作物育种智能分析算法开发（横向项目）	项目负责人（乔雷洁）
2024.01-2026.12	带有弱奇异核的非局部方程高效数值方法研究（山西省自然科学基金面上项目）	项目负责人（乔雷洁）
2022.01–2024.12	非光滑初值时间分数阶积分微分方程高阶数值方法研究（国家自然科学基金青年科学基金项目）	项目负责人（乔雷洁）
2022.01–2022.12	非局部微积分方程高阶数值方法研究（国家自然科学基金天元数学访问学者项目）	项目负责人（乔雷洁）
2022.01-2024.12	非光滑粘弹性方程的高阶数值方法研究（湖南省科技厅一般项目）	项目负责人（乔雷洁）
2022.01-2024.12	三维复合粘弹性问题的高效数值方法研究（湖南省自然科学基金青年基金项，）	项目负责人（乔雷洁）
2019.04-2022.03	时间分数阶Klein-Gordon方程的高精度快速算法研究（广州市科学研究计划一般项目）	项目参与者
2019.10-2022.10	基于非均匀网格技术的时间分数阶方程的高效数值方法研究（广东省自然科学基金面上项目）	项目参与者
2017.01-2020.12	带多项复合型粘弹性材料弯曲波问题有限元方法（国家自然科学基金面上项目）	项目参与者
2016.01–2018.02	偏微分方程解的数值研究（湖南师范大学研究生科研创新项目）	项目负责人（乔雷洁）

荣誉和获奖

2025.08-2028.08     山西省青年拔尖人才

2024.06-2026.06     山西大学青年文瀛学者

教学

1.数学分析（上），2022年秋.

2.数学分析（下），2023年春.

3.偏微分方程数值解，2025年春.

学术论文

*为通讯作者。

[1]L. Qiao, D. Xu, W. Qiu*, A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem, Comput. Math. Appl. 102 (2021) 137-145.

[2]L. Qiao, B. Tang*, An accurate, robust, and efficient finite difference scheme with graded meshes for the time-fractional Burgers’ equation, Appl. Math. Lett. 128 (2022) 107908. (T3)

[3]L. Qiao, D. Xu, Z. Wang*, An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation, Appl. Numer. Math. 151 (2020) 199-212.

[4]L. Qiao, D. Xu, Y. Yan, High-order ADI orthogonal spline collocation method for a new 2D fractional integro-differential problem, Math. Meth. Appl. Sci. 43(2020) 5162-5178.(T3)

[5]L. Qiao*, D. Xu, A fast ADI orthogonal spline collocation method with graded meshes for the two-dimensional fractional integro-differential equation, Adva. Comput. Math. 47(2021), 64. (T2)

[6]L. Qiao, D. Xu, B. Tang*, J. Zhou, Fast ADI difference/compact difference schemes for the nonlocal evolution equation with weakly singular kernels in three dimensions, Math. Comput. Simu. 194 (2021) 329-347. (T2)

[7]L. Qiao*, D. Xu, Orthogonal spline collocation method for the two-dimensional time fractional mobile-immobile equation, J. Appl. Math. Comp. 68 (2022) 3199-3217.

[8]L. Qiao, W. Qiu*, D. Xu, Error analysis of fast L1 ADI finite difference/compact difference schemes for the fractional telegraph equation in three dimensions, Math. Comput. Simu. 205 (2023) 205-231. (T2)

[9]L. Qiao, B. Tang*, D. Xu, W. Qiu, High-order orthogonal spline collocation method with graded meshes for two-dimensional fractional evolution integro-differential equation, Int. J. Comput. Math. 99 (2022) 1305-1322.

[10]L. Qiao, D. Xu, Z. Wang*, Orthogonal spline collocation method for the two-dimensional time fractional mobile-immobile equation, J. Appl. Math. Comput. 68 (2022) 3199-3217.

[11]L. Qiao, O. Nikan, Z. Avazzadeh*, Some efficient numerical schemes for approximating the nonlinear two-space dimensional extended Fisher-Kolmogorov equation, Appl. Numer. Math. 185 (2023) 466-482. (T2)

[12]L. Qiao, W. Qiu*, D. Xu, Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion, Numer. Algor. 93(2023), 1083-1104. (T2)

[13]L. Qiao, W. Qiu*, B. Tang, A fast numerical solution of the 3D nonlinear tempered fractional integrodifferential equation, Numer. Methods Part. Differ. Equ. 39 (2023) 1333-1354. (T3)

[14]J. Zhou, D. Xu, W. Qiu, L. Qiao*, An accurate, robust, and efficient weak Galerkin finite element scheme with graded meshes for the time-fractional quasi-linear diffusion equation, Comput. Math. Appl. 124 (2022) 188-195.

[15]L. Qiao*, D. Xu, BDF ADI orthogonal spline collocation scheme for the fractional integro- differential equation with two weakly singular kernels, Comput. Math. Appl. 78 (2019) 3807-3820.

[16]L. Qiao, Z. Wang*, D. Xu, An ADI finite difference scheme based on fractional trapezoidal rule for fractional integro-differential equation with a weakly singular kernel, Appl. Math. Comput. 354 (2019) 103-114.

[17]L. Qiao*, D. Xu, Orthogonal spline collocation scheme for the multi-term time fractional diffusion equation, Int. J. Comput. Math. 95 (2018) 478-1493.

[18]L. Qiao*, D. Xu, Compact alternating direction implicit scheme for integro-differential equations of parabolic type, J. Sci. Comput. 76 (2018) 565-582.

[19]B. Tang*, L. Qiao, D. Xu, An ADI orthogonal spline collocation method for a new two-dimensional distributed-order fractional integro-differential equation, Comput. Math. Appl. 132 (2023) 104-118.

[20]Q. Huang, L. Qiao, B. Tang*, High-order orthogonal spline collocation ADI scheme for a new complex two-dimensional distributed-order fractional integro-differential equation with two weakly singular kernels, Int. J. Comput. Math. 100 (2023) 703-721.

[21]X. Fang, L. Qiao, F. Zhang, F. Sun, Explore deep network for a class of fractional partial differential equations, Chaos Solit. Fract.172 (2023)113528.

[22]L. Qiao, D. Xu, W. Qiu, The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space, Appl. Numer. Math. 172 (2022) 359-381. (T2)

[23]L. Qiao, J. Guo, W. Qiu, Fast BDF2 ADI methods for the multi-dimensional tempered fractional integrodifferential equation of parabolic type, Comput. Math. Appl. 123 (2022) 89-104.

[24]R. Wang, L. Qiao*, A. Zaky, A. Hendy, A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions, Numer. Algor.

95 (2024): 319-349.. (2023).(T2)

[25]A. Hendy, L. Qiao, A. Aldraiweesh , Optimal spectral Galerkin approximation for time and space

fractional reaction-diffusion equations, Appl. Numer. Math. 201 (2024) 118-128.(T2)

[26]R. Wang, Y. Yan, A. Hendy, L. Qiao*, BDF2 ADI orthogonal spline collocation method for the

fractional integro-differential equations of parabolic type in three dimensions, Comput. Math. Appli. 155 (2024) 126-141.

[27]R. Wang, L. Qiao*, A. Zaky, A second-order finite difference scheme for nonlinear tempered

fractional integrodifferential equations in three dimensions, Numer. Algor. 95 (2024) 319-349.

[28]L. Qiao, A. Zaky, A. Hendy, W. Qiu, Theta-type convolution quadrature OSC method for nonlocal

evolution equations arising in heat conduction with memory, Fract. Calc. Appl. Anal. 27(2024), 1136-1161.

[29]HO Sidi, AS Hendy, MM Babatin, L Qiao, MA Zaky，An inverse problem of Robin coefficient

identification in parabolic equations with interior degeneracy from terminal observation data，Appl. Numer. Math. 212 (2025) 242-253.

[30]Y. Tang, L. Qiao, X. Guan, Parameter Identification of Wiener Model with Discontinuous Nonlinearities Using Hybrid Simplex Search and Particle Swarm Optimization, NeuroQuantology, 6 (2008) 387-396.

[31]Y. Tang, L. Qiao, X. Guan, Identification of Wiener model using step signals and particle swarm optimization, Expert Syst. Appl., 37 (2010) 3398-3404.

[32]L.Qiao, D. Xu. Orthogonal spline collocation scheme for the multi-term time-fractional diffusion equation,Int. J. Comput. Math. 95 (2018) 1478-1493.

[33]R. Wang, Y. Chen, L. Qiao, An efficient variable step numerical method for the three-dimensional

nonlinear evolution equation, J. Appl. Math. Comput. 70 (2024) 6131-6163.