Milstein method for solving fuzzy differential equation

被引：0
|
作者：
Ji, L. Y. [1 ]
You, C. L. [2 ]
机构：
[1] Hebei Univ, Coll Math & Informat Sci, Baoding 071002, Peoples R China
[2] Hebei Univ, Hebei Key Lab Machine Learning & Computat Intelli, Baoding 071002, Peoples R China
来源：
IRANIAN JOURNAL OF FUZZY SYSTEMS | 2021年 / 18卷 / 03期
关键词：
Credibility; fuzzy differential equation; Milstein method; semi-implicit Milstein method; improved Milstein method; mean-stability; CREDIBILITY; STABILITY;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analyzed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.
引用
收藏
页码：129 / 141
页数：13
相关论文
共 50 条
  • [21] Convergence rate of the truncated Milstein method of stochastic differential delay equations
    Zhang, Wei
    Yin, Xunbo
    Song, M. H.
    Liu, M. Z.
    APPLIED MATHEMATICS AND COMPUTATION, 2019, 357 : 263 - 281
  • [22] SPLIT-STEP FORWARD MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS
    Sinch, Samar
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2012, 9 (04) : 970 - 981
  • [23] The variational iteration method for solving a neutral functional-differential equation with proportional delays
    Chen, Xumei
    Wang, Linjun
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (08) : 2696 - 2702
  • [24] ON STEADY-STATE SOLUTIONS OF A WAVE EQUATION BY SOLVING A DELAY DIFFERENTIAL EQUATION WITH AN INCREMENTAL HARMONIC BALANCE METHOD
    Wang, Xuefeng
    Liu, Mao
    Zhu, Weidong
    PROCEEDINGS OF THE ASME 11TH ANNUAL DYNAMIC SYSTEMS AND CONTROL CONFERENCE, 2018, VOL 3, 2018,
  • [25] THE TRUNCATED MILSTEIN METHOD FOR SUPER-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH MARKOVIAN SWITCHING
    Zhan, Weijun
    Guo, Qian
    Cong, Yuhao
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2022, 27 (07): : 3663 - 3682
  • [26] The Behavior of Logistic Equation with Alley Effect in Fuzzy Environment: Fuzzy Differential Equation Approach
    Salahshour S.
    Ahmadian A.
    Mahata A.
    Mondal S.P.
    Alam S.
    International Journal of Applied and Computational Mathematics, 2018, 4 (2)
  • [27] An Improved Runge-Kutta Method for Solving Fuzzy Differential Equations Under Generalized Differentiability
    Ahmadian, Ali
    Suleiman, Mohamed
    Ismail, Fudziah
    Salahshour, Soheil
    INTERNATIONAL CONFERENCE ON FUNDAMENTAL AND APPLIED SCIENCES 2012 (ICFAS2012), 2012, 1482 : 325 - 330
  • [28] Modified variational iteration method for solving a neutral functional-differential equation with proportional delays
    Ghaneai, H.
    Hosseini, M. M.
    Mohyud-Din, Syed Tauseef
    INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 2012, 22 (08) : 1086 - 1095
  • [29] A RANDOMIZED MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-DIFFERENTIABLE DRIFT COEFFICIENTS
    Kruse, Raphael
    Wu, Yue
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08): : 3475 - 3502
  • [30] SOLUTIONS OF FUZZY DIFFERENTIAL EQUATION WITH FUZZY NUMBER COEFFICIENT BY FUZZY LAPLACE TRANSFORM
    Citil, Hulya Gultekin
    COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2020, 73 (09): : 1191 - 1200
12345