教师名录
梁慧
通讯地址:深圳大学城哈工大校区G1012
电子邮件:lianghui@hit.edu.cn; wise2peak@126.com
联系电话:18800465586

个人简介

梁慧,博士,教授。2008年7月获哈尔滨工业大学数学博士学位。2010.3.1-2011.9.31 在香港浸会大学担任客座研究学人,并多次访问香港浸会大学。2017.12.1-2018.11.30在加拿大纽芬兰纪念大学(Memorial University of Newfoundland) 担任访问学者。2008年开始在黑龙江大学工作,2019年转入哈尔滨工业大学(深圳)工作。任SCI期刊Computational & Applied Mathematics编委、中国仿真学会仿真算法专委会委员、黑龙江省数学会理事。主要的研究方向为:延迟微分方程、Volterra积分方程的数值分析。主持国家自然科学基金、青年基金、黑龙江省普通本科高等学校青年创新人才培养计划等9项科研项目,获中国系统仿真学会“2015年优秀论文”奖、2018第二届黑龙江省数学会优秀青年学术奖。目前共被SCI收录文章26篇,其中JCR一区15篇,发表在SIAM Journal on Numerical Analysis 、IMA Journal of Numerical Analysis、Journal of Scientific Computing、BIT Numerical Mathematics、Advances in Computational Mathematics、Applied Numerical Mathematics 等15种不同的国际杂志上。

研究方向

Volterra积分及积分微分方程的数值分析
延迟微分方程的数值分析
随机Volterra积分方程的数值分析
分数阶微分方程的数值分析

教育经历

2005.8-2008.7  哈尔滨工业大学 博士
2002.9-2005.7  郑州大学 硕士
1998.9-2002.7  郑州大学 学士

研究与工作经历

2019.2-至今  哈尔滨工业大学(深圳) 教授
2015.9-2019.1  黑龙江大学 教授
2010.9-2015.8  黑龙江大学 副教授
2008.7-2010.8  黑龙江大学 讲师
2017.12.1-2018.11.30  加拿大纽芬兰纪念大学 访问学者
2017.8.1-2017.8.15  香港浸会大学 客座研究学人
2016.6.30-2016.7.29  香港浸会大学 客座研究学人
2015.3.9-2015.4.8  香港浸会大学 客座研究学人
2010.3.1-2011.9.31  香港浸会大学 客座研究学人
2009.2.27-2009.5.26  香港浸会大学 博士后研究学人

专业资质与学术兼职

2018.4-至今  SCI期刊Computational & Applied Mathematics 编委
2015.9-至今  中国仿真学会仿真算法专委会 委员
2014.8-至今  黑龙江省数学会 理事

科研项目

2018.1-2021.12  国家自然科学基金面上项目,几类Volterra积分代数方程及积分微分代数方程的理论及配置方法研究,48万(直接经费),主持
2019.1-2021.12  校科研启动经费,几类积分微分代数方程的数值方法研究,20万,主持
2012.1-2014.12  国家自然科学基金青年基金资助项目,延迟脉冲微分方程和Volterra积分方程的hp-谱配置方法,23万,主持

科研成果及奖励

2015.12.1   梁慧,Hermann Brunner,论文《Integral-algebraic equations: theory of collocation methods I》被中国系统仿真学会评选为“2015年优秀论文”。(获奖论文详细信息:Hui Liang, Hermann Brunner, Integral-algebraic equations: theory of collocation methods I, SIAM Journal on Numerical Analysis (SCI), 2013, 51: 2238-2259)
2018  第二届黑龙江省数学会优秀青年学术奖
2012.2.21  宋明辉,杨占文,梁慧,高建芳,刘明珠,《延迟微分方程、随机延迟微分方程和脉冲微分方程数值分析》获黑龙江省高校科学技术一等奖。

论文及著作

论文

[27] Hui Liang, Hermann Brunner, The convergence of collocation solutions in continuous piecewise polynomial spaces for weakly singular Volterra integral equations, SIAM Journal on Numerical Analysis, 2019, accepted.

[26] Hui Liang, Hermann Brunner, Collocation methods for integro-differential algebraic equations with index-1, IMA Journal of Numerical Analysis, 2019, online.

[25] Jianfang Gao, Hui Liang, Shufang Ma, Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay, Applied Mathematics and Computation, 2019, 384: 385-398. 通讯作者

[24] Jianfang Gao, Shufang Ma, Hui Liang, Strong convergence of the semi-implicit Euler method for a kind of stochastic Volterra integro-differential equations, Numerical Mathematics Theory Methods and Applications, 2019, 12(2): 547-565.

[23] Hui Liang, Martin Stynes, Collocation methods for general Riemann-Liouville two-point boundary value problems, Advances in Computational Mathematics, 2019, 45: 897-928.

[22] Hui Liang, Martin Stynes, Collocation methods for general Caputo two-point boundary value problems, Journal of Scientific Computing, 2018, 76: 390-425.

[21] Tingting Zhang, Hui Liang, Multistep collocation approximations to solutions of first-kind Voterra integral equations, Applied Numerical Mathematics, 2018, 130: 171-183. 通讯作者,第一作者为硕士研究生

[20] Hui Liang, Zhanwen Yang, Jianfang Gao, Strong superconvergence of the Euler-Maruyama method for linear stochastic Volterra integral equations, Journal of Computational and Applied Mathematics, 2017, 317: 447-457.

[19] Hui Liang, hp-Legendre-Gauss collocation method for impulsive differential equations, International Journal of Computer Mathematics, 2017, 94: 151-172. 独立作者

[18] Hui Liang, Hermann Brunner, Integral-algebraic equations: theory of collocation methods II, SIAM Journal on Numerical Analysis, 2016, 54: 2640-2663.

[17] Ran Zhang, Hui Liang, Hermann Brunner, Analysis of collocation methods for generalized auto-convolution Volterra integral equations, SIAM Journal on Numerical Analysis, 2016, 54: 899-920. 通讯作者

[16] Hui Liang, Hermann Brunner, On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations, BIT Numerical Mathematics, 2016, 56: 1339-1367.

[15] Hui Liang, Convergence and asymptotic stability of Galerkin methods for linear parabolic equations with delays,Applied Mathematics and Computation, 2015, 264: 160-178. 独立作者

[14] Hui Liang, Mingzhu Liu, Zhanwen Yang, Stability analysis of Runge-Kutta methods for systems u'(t)=Lu(t)+Mu([t]), Applied Mathematics and Computation, 2014, 228: 336-348.

[13] Zuhua Zhang, Hui Liang, Collocation methods for impulsive differential equations, Applied Mathematics and Computation, 2014, 228: 463-476. 通讯作者,第一作者为硕士研究生

[12] Hui Liang, Hermann Brunner, Integral-algebraic equations: theory of collocation methods I, SIAM Journal on Numerical Analysis, 2013, 51: 2238-2259.

[11] Hui Liang, Hermann Brunner, Discrete superconvergence of collocation solutions for first-kind Volterra integral equations, Journal of Integral Equations and Applications, 2012, 3(24): 359-391.

[10] Hui Liang, Hermann Brunner, Collocation methods for differential equations with piecewise linear delays, Communications on Pure and Applied Analysis, 2012, 5(11): 1839-1857.

[9] Hui Liang, Minghui Song, Mingzhu Liu, Stability of the analytic and numerical solutions for impulsive differential equations, Applied Numerical Mathematics, 2011, 61(11): 1103-1113.

[8] Hui Liang, Mingzhu Liu, Minghui Song, Extinction and permanence of Euler methods in the numerical solution of a two-prey one-predator system with impulsive effect, International Journal of Computer Mathematics, 2011, 88: 1305-1325.

[7] Hermann Brunner, Hui Liang, Stability of collocation methods for delay differential equations with vanishing delays, BIT Numerical Mathematics, 2010, 50: 693-711.

[6] Hui Liang, Mingzhu Liu, Wanjin Lv, Stability of θ-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments, Applied Mathematics Letters, 2010, 23: 198-206.

[5] Hui Liang, Dongyang Shi, Wanjin Lv, Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument, Applied Mathematics and Computation, 2010, 217(2): 854-860.

[4] Dongyang Shi, Hui Liang, Convergence and superconvergence analysis of a new quadratic Hermite-type triangular element on anisotropic meshes, Applied Mathematics and Computation, 2009, 212: 257-269.

[3] Mingzhu Liu, Hui Liang, Zhanwen Yang, Stability of Runge-Kutta methods in the numerical solution of linear impulsive differential equations, Applied Mathematics and Computation, 2007, 192(2): 346-357.

[2] Dongyang Shi, Hui Liang, Superconvergence analysis of Wilson’s element on anisotropic meshes, Applied Mathematics and Mechanics, 2007, 28(1): 119-125.

[1] Dongyang Shi, Hui Liang, Caixia Wang, Superconvergence analysis of a nonconforming triangular element on anisotropic meshes, Journal of Systems Science and Complexity, 2007, 20: 536-544.

专著

1. 梁慧,《几类微分方程数值方法的研究》, 哈尔滨工业大学出版社, 2015年.

会议论文及发表演说

[24] 华中科技大学,武汉,2019. 06. 15
报告题目:Integro-differential algebraic equations: theory of collocation methods

[23] The 14th SIAM East Asian Section Conference (EASIAM), 武汉,2019. 06. 13-16
报告题目:On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations

[22] 南方科技大学,深圳,2019. 06. 06
报告题目:Integro-differential algebraic equations: theory of collocation methods

[21] 西南财经大学经济数学学院,成都,2019. 05. 18
报告题目:Collocation methods for general Caputo and Riemann-Liouville two-point boundary value problems

[20] 北京工业大学,北京,2019. 04. 28
报告题目:Analysis of collocation methods for index-1 integro-differential algebraic equations

[19] 3rd CSRC Workshop Numerical Methods for Fractional-Derivative Problems, 北京,2019. 04. 26-27
报告题目:Collocation methods for general Riemann-Liouville two-point boundary value problems

[18] 中国科学院数学与系统科学研究院,北京,2019. 04. 24
报告题目:Collocation methods for integro-differential algebraic equations with index-1

[17] The 25th International Domain Decomposition Conference (DD25), St. John’s (加拿大圣约翰斯), 2018. 07. 23-27
报告题目:Theory and collocation solvers for Integral-algebraic equations

[16] International Workshop on Numerical Analysis of Differential and Integral Equations (微分及积分方程数值分析国际研讨会),哈尔滨,2017. 08. 20-23
报告题目:Some recent work on theory of collocation methods for integral-algebraic equations

[15] 第十五届微分方程数值方法学术会议暨第十二届仿真算法会议,海口,2017. 08. 15-18
报告题目:On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations

[14] 长沙理工大学数学与统计学院,长沙,2017. 05. 11
报告题目:Integral-algebraic equations: theory of collocation methods

[13] 湘潭大学数学与计算科学学院,湘潭,2017. 05. 08
报告题目:Integral-algebraic equations: theory of collocation methods

[12] 20th IMACS World Congress, 厦门,2016. 12. 10-14
报告题目:Integral-algebraic equations: theory of collocation methods

[11] 2016年北京科学与工程计算研究院计算数学青年学者论坛,北京,2016. 10. 28-29
报告题目:Integral-algebraic equations: theory of collocation methods

[10] 黑龙江省数学学会第十四届年会,齐齐哈尔,2016. 08.14-16
报告题目: Integral-algebraic equations: theory of collocation methods

[9] 中国科学院数学与系统科学研究院计算数学所,北京,2016. 05. 18
报告题目:Integral-algebraic equations: theory of collocation methods

[8] 北京计算科学研究中心,北京,2016. 05. 12
报告题目:Integral-algebraic equations: theory of collocation methods

[7] 第十一届全国微分方程数值方法暨第十一届全国仿真算法学术会议,哈尔滨,2015. 07. 13-16
报告题目:Integral-algebraic equations: theory of collocation methods I

[6] 香港理工大学数学系,香港,2015. 03. 31
报告题目:Integral-algebraic equations: theory of collocation methods I

[5] 黑龙江省数学会第十二届年会,佳木斯,2012. 08.04-06
报告题目:Stability of collocation methods for delay differential equations with vanishing delays

[4] SCPDE11 The 4th. International Conference on Scientific Computing and Partial Differential Equations, 香港,2011. 12. 04-09
报告题目:Stability of collocation methods for delay differential equations with vanishing delays

[3] 吉林大学数学学院,长春,2011. 10. 28
报告题目:Stability of collocation methods for delay differential equations with vanishing delays

[2] 黑龙江省计算数学年会暨哈尔滨地区计算数学研讨会,哈尔滨,2009. 12. 19
报告题目:Numerical analysis of a partial differential equation with piecewise constant argument.

[1] 黑龙江省数学会第十届年会,牡丹江,2008. 07. 25-27
报告题目:Stability of Runge-Kutta methods in the numerical solution of linear impulsive differential equations

任教和任导师经历

曾经讲授过的部分课程: [1] 本科生课程:   常微分方程、数学物理方程、数值代数、微分方程数值解、计算方法引论、专业导读、高等数学、职业生涯规划、漫谈科学计算

[2] 研究生课程:   线性多步法与Runge-Kutta方法、Volterra积分方程的配置方法、泛函微分方程数值方法、论文选读

已毕业获得硕士学位研究生:   李金玲、王帅、李美丽、杨丽晶、阚智坚、刘洋、张婷婷、王哲、张宇佳
最后更新:2019-06-19 15:22:37