Renormalization group approach to a class of singularly perturbed delay differential equations

被引：4
作者：
Xu, Lin [1 ]
Xu, Zhiguo [1 ]
Li, Wenlei [1 ]
Shi, Shaoyun [1 ,2 ]
机构：
[1] Jilin Univ, Sch Math, Changchun 130012, Peoples R China
[2] Jilin Univ, State Key Lab Automot Simulat & Control, Changchun 130012, Peoples R China
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2021年 / 103卷
关键词：
Renormalization group method; Singularly perturbed delay differential equation; Error estimate; Numerical simulation; BOUNDARY-VALUE-PROBLEMS; SMALL SHIFTS; LAYER;
D O I：
10.1016/j.cnsns.2021.106028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present a systematic renormalization group method to investigate a class of singularly perturbed delay differential equations. The uniformly valid approximate solution can be obtained, and we give a rigorous proof of the error estimate of the approximate solution. In addition, some numerical comparisons between the exact solution, the result by the averaging method and our result are given for two examples. (C) 2021 Elsevier B.V. All rights reserved.
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页数：11
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共 26 条
  • [1] Analytical prediction of chatter stability in milling - Part 1: General formulation
    Budak, E
    Altintas, Y
    [J]. JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 1998, 120 (01): : 22 - 30
  • [2] Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory
    Chen, LY
    Goldenfeld, N
    Oono, Y
    [J]. PHYSICAL REVIEW E, 1996, 54 (01): : 376 - 394
  • [3] RENORMALIZATION-GROUP THEORY FOR GLOBAL ASYMPTOTIC ANALYSIS
    CHEN, LY
    GOLDENFELD, N
    OONO, Y
    [J]. PHYSICAL REVIEW LETTERS, 1994, 73 (10) : 1311 - 1315
  • [4] C1 Approximation of Vector Fields Based on the Renormalization Group Method
    Chiba, Hayato
    [J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2008, 7 (03) : 895 - 932
  • [5] Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method
    Chiba, Hayato
    [J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2009, 8 (03): : 1066 - 1115
  • [6] Approximation of center manifolds on the renormalization group method
    Chiba, Hayato
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (10)
  • [7] BIFURCATION GAP IN A HYBRID OPTICALLY BISTABLE SYSTEM
    DERSTINE, MW
    GIBBS, HM
    HOPF, FA
    KAPLAN, DL
    [J]. PHYSICAL REVIEW A, 1982, 26 (06): : 3720 - 3722
  • [8] Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations
    DeVille, R. E. Lee
    Harkin, Anthony
    Holzer, Matt
    Josic, Kresimir
    Kaper, Tasso J.
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2008, 237 (08) : 1029 - 1052
  • [9] Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group
    Dutta, Ayan
    Das, Debapriya
    Banerjee, Dhruba
    Bhattacharjee, Jayanta K.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 57 : 47 - 57
  • [10] Renormalization reductions for systems with delay
    Goto, Shin-itiro
    [J]. PROGRESS OF THEORETICAL PHYSICS, 2007, 118 (02): : 211 - 227
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