JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (12): 32-37.doi: 10.6040/j.issn.1671-9352.0.2023.424

Previous Articles     Next Articles

Application of matrix theory in solving a class of differential equations

CAO Haisong, WANG Chenxu, LI Hengyan   

  1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450045, Henan, China
  • Published:2025-12-10

PDF (PC)

84

Abstract: From the perspective of matrix, this paper discusses the application of matrix theory in solving a class of differential equations, and its effectiveness is verified by numerical examples.

Key words: matrix theory, diagonalization, Jordan matrix, matrix function, differential equation

CLC Number: 

  • O29
[1] 张贤达. 矩阵分析与应用[M]. 2版. 北京:清华大学出版社,2013:325. ZHANG Xianda. Matrix analysis and application[M]. 2nd ed. Beijing: Tsinghua University Press, 2013:325.
[2] 李尚志. 线性代数精彩应用案例(之一)[J]. 大学数学,2006,22(3):1-8. LI Shangzhi. Wonderful application cases of linear algebra(1)[J]. College Mathematics, 2006, 22(3):1-8.
[3] GILBERT S. Introduction to linear algebr[M]. 4th ed. Massachusetts: Wellesley-Cambridge Press, 2009:33-37.
[4] 杨明,刘先忠. 矩阵论[M]. 2版. 武汉:华中科技大学出版社,2014:40-43. YANG Ming, LIU Xianzhong. Matrix theory[M]. 2nd ed. Wuhan: Huazhong University of Science and Technology Press, 2014.
[5] 廖晓花. 三元一阶线性非齐次微分方程组解法分析[J]. 兰州工业学院学报,2021,28(1):86-91. LIAO Xiaohua. Solution analysis of first order linear non-homogeneous differential equations with three variables[J]. Journal of Lanzhou Institute of Technology, 2021, 28(1):86-91.
[6] 杨景保,莫嘉琪. 一类非线性三阶微分方程边值问题解的存在唯一性[J]. 应用数学和力学,2020,41(2):216-222. YANG Jingbao, MO Jiaqi. Existence and uniqueness of solutions to boundary value problems of a class of nonlinear 3rd-order differential equations[J]. Applied Mathematics and Mechanics, 2020, 41(2):216-222.
[7] 周恺,高芳,朱立明. 一类特殊的二阶常系数线性非齐次微分方程的解法[J]. 赤峰学院学报(自然科学版),2018,34(7):167-168. ZHOU Kai, GAO Fang, ZHU Liming. Solution of a special second-order linear non-homogeneous differential equation with constant coefficients[J]. Journal of Chifeng University(Natural Science Edition), 2018, 34(7):167-168.
[8] 李迎娣. 二阶常系数线性非齐次微分方程的一些解法[J]. 中央民族大学学报(自然科学版),2018,27(1):21-23. LI Yingdi. Some solutions to the second order constant coefficient Linea nonhomogeneous differential equation[J]. Journal of Minzu University of China(Natural Sciences Edition), 2018, 27(1):21-23.
[9] 栾新,辛佳,宋大雷,等. 分数阶微分方程组的一种高精度数值算法[J]. 系统仿真学报,2018,30(2):421-426. LUAN Xin, XIN Jia, SONG Dalei, et al. High order numerical method for system of fractional differential equations[J]. Journal of System Simulation, 2018, 30(2):421-426.
[10] KANGUZHIN B K, NURAKHMETOV D B. Boundary value problems for 2nd order non-homogeneous differential equations with variable coefficients[J]. Journal of Xinjiang University(Natural Science Edition), 2011(1):47-56.
[11] 胡劲松. 一阶高次齐次微分方程的求解[J]. 大学数学,2010,26(4):169-172. HU Jinsong. Solving one-order homogeneous differential equation of higher degree[J]. College Mathematics, 2010, 26(4):169-172.
[12] 李俊,周文. 可对角化矩阵的应用[J]. 数学学习与研究,2020(5):16-17. LI Jun, ZHOU Wen. Application of diagonalizable matrix[J]. Mathematics Learning and Research, 2020(5):16-17.
[13] 冯俊娥,张庆乐. 齐次线性常微分方程组基于过渡矩阵的求解方法[J]. 大学数学,2020,36(6):55-62. FENG June, ZHANG Qingle. A method for solving homogeneous linear ordinary differential equations based on transition matrix[J]. College Mathematics, 2020, 36(6):55-62.
[1] LI Aoyu. Traveling wave solutions of a class of SEIR lattice differential equations with saturated recovery rate [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(8): 106-115.
[2] ZHENG Yanping, YANG Hui, WANG Wenxia. The existence of unique positive solution for boundary value problems of fractional differential equations with parameters and derivatives involving p-Laplacian operators [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 110-120.
[3] XU Yinuo, LIU Libin, YANG Xiu. Adaptive moving grid method for a second-order singularly perturbed delay boundary value problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 84-93.
[4] XI Xia, LI Yongxiang. Periodic solutions of a second-order delay ordinary differential equation with derivative term [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 103-109.
[5] Fangfang HU,Weimin HU,Yong ZHANG. Existence and uniqueness of positive solutions of integral boundary value problems for a class of fractional differential equations with Hadamard derivatives [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 53-61.
[6] XIANG Xuxu, LIU Jianming, WANG Qin, OUYANG Ruiqi. Julia limiting directions of entire solutions of complex differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 73-78.
[7] LIU Huijuan. Existence of one-signed solutions for three-point boundary value problems of second-order differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 79-86.
[8] Haodong LIU,Chi ZHANG. Optimal monetary policy with a zero lower bound on the nominal interest rate under a continuous-time framework [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(1): 11-16.
[9] Yejun CHEN,Huisheng DING. θ-almost periodic solutions for stochastic differential equations in infinite dimensions with Stepanov almost periodic coefficients [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 113-126.
[10] ZHAO Xia, ZHU Yi-pin, YANG Ya-jie, XU Lan-tao. Portfolio research based on temporal network and random matrix theory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(1): 101-110.
[11] LI Ning, GU Hai-bo, MA Li-na. Existence of solutions for boundary value problems of a class of nonlinear Caputo type sequential fractional differential equations on star graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(7): 22-34.
[12] WANG Xiao-huan, LÜ Guang-ying, DAI Li-jie. Generalization of Gronwalls inequality and applications [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(6): 94-101.
[13] XI Yan-li, CHEN Peng-yu. Uniqueness of solutions for initial value problems of implicit fractional order fuzzy differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 85-90.
[14] WANG Miao-miao, DING Xiao-li, LI Jia-min. Waveform relaxation methods for fractional stochastic delay differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(1): 101-110.
[15] XUE Ting-ting, XU Yan, LIU Xiao-ping. Existence of nontrivial weak solutions for fractional boundary value problems with variable coefficients [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 45-51.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] ZHANG Dong-qing, YIN Xiao-bin, GAO Han-peng. Quasi-linearly Armendariz modules[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 1 -6 .
[2] ZHANG Liang,WANG Hai-mei,HUANG He-yan,ZHANG Xiao-fei . Chinese question answering systemoriented Chinese parsing[J]. J4, 2006, 41(3): 30 -33 .
[3] ZHANG Shen-gui. Multiplicity of solutions for local superlinear p-kirchhoff-type equation#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(05): 61 -68 .
[4] WAN Hai-ping,HE Hua-can,ZHOU Yan-quan . Locality preserving kernel method and its application[J]. J4, 2006, 41(3): 18 -20 .
[5] WANG Guang-chen . LQ nonzero sum stochastic differential game under partial observable information[J]. J4, 2007, 42(6): 12 -15 .
[6] HU Shu-min,KONG Jian,JI Ming-jie* .

Screening of broad-spectrum bacteriocin-producing lactic acid bacteria

[J]. J4, 2008, 43(7): 61 -64 .
[7] YANG Jun. Characterization and structural control of metalbased nanomaterials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 1 -22 .
[8] DONG Wei-wei. A new method of DEA efficiency ranking for decision making units with independent subsystems[J]. J4, 2013, 48(1): 89 -92 .
[9] YE Cheng-fu and YIN Jian . The chromatically equivalent depiction and the chromatically unique condition of the complement of Pl∪Cm∪Dn[J]. J4, 2006, 41(1): 24 -29 .
[10] WU Chun-fu1, TANG Qing-shun1, XIE Huang-sheng1, ZHOU Feng-yu2*. A novel analytical essential matrix decomposition algorithm#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 31 -36 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd