A Collocation Method for the Numerical Solution of Nonlinear Fractional Dynamical Systems

被引：7
作者：
Pitolli, Francesca [1 ,2 ]
机构：
[1] Univ Roma La Sapienza, Dept SBAI, I-00161 Rome, Italy
[2] Via Antonio Scarpa 16, I-00161 Rome, Italy
来源：
ALGORITHMS | 2019年 / 12卷 / 08期
关键词：
fractional differential equation; nonlinear dynamical system; B-spline; collocation method;
D O I：
10.3390/a12080156
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Fractional differential problems are widely used in applied sciences. For this reason, there is a great interest in the construction of efficient numerical methods to approximate their solution. The aim of this paper is to describe in detail a collocation method suitable to approximate the solution of dynamical systems with time derivative of fractional order. We will highlight all the steps necessary to implement the corresponding algorithm and we will use it to solve some test problems. Two Mathematica Notebooks that can be used to solve these test problems are provided.
引用
收藏
页数：13
相关论文
共 50 条
  • [21] NUMERICAL SOLUTION OF THE NONLINEAR KORTEWEG-DE VRIES EQUATION BY USING CHEBYSHEV WAVELET COLLOCATION METHOD
    Bakir, Yasemin
    HONAM MATHEMATICAL JOURNAL, 2021, 43 (03): : 373 - 383
  • [22] Numerical solution of Burgers' equation by cubic Hermite collocation method
    Ganaie, I. A.
    Kukreja, V. K.
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 237 : 571 - 581
  • [23] Numerical solution of the static beam problem by Bernoulli collocation method
    Ren, Quanwei
    Tian, Hongjiong
    APPLIED MATHEMATICAL MODELLING, 2016, 40 (21-22) : 8886 - 8897
  • [24] Numerical solution of the diffusion problem of distributed order based on the Sinc-collocation method
    Taherkhani, Sh
    Khalilsaraye, I. Najafi
    Ghayebi, B.
    MATHEMATICAL SCIENCES, 2023, 17 (02) : 133 - 144
  • [25] Numerical solution of the diffusion problem of distributed order based on the Sinc-collocation method
    Sh. Taherkhani
    I. Najafi Khalilsaraye
    B. Ghayebi
    Mathematical Sciences, 2023, 17 : 133 - 144
  • [26] Numerical Solution of the Fractional Order Duffing–van der Pol Oscillator Equation by Using Bernoulli Wavelets Collocation Method
    Rahimkhani P.
    Moeti R.
    International Journal of Applied and Computational Mathematics, 2018, 4 (2)
  • [27] Efficient sustainable algorithm for numerical solutions of systems of fractional order differential equations by Haar wavelet collocation method
    Abdeljawad, Thabet
    Amin, Rohul
    Shah, Kamal
    Al-Mdallal, Qasem
    Jarad, Fahd
    ALEXANDRIA ENGINEERING JOURNAL, 2020, 59 (04) : 2391 - 2400
  • [28] NUMERICAL SOLUTION OF FRACTIONAL RELAXATION-OSCILLATION EQUATION USING CUBIC B-SPLINE WAVELET COLLOCATION METHOD
    Chandel, Raghvendra S.
    Singh, Amardeep
    Chouhan, Devendra
    ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2016, (36): : 399 - 414
  • [29] Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrodinger equations
    Doha, E. H.
    Bhrawy, A. H.
    Abdelkawy, M. A.
    Van Gorder, Robert A.
    JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 261 : 244 - 255
  • [30] Numerical solution of two-dimensional linear and nonlinear Volterra integral equations using Taylor collocation method
    Laib, Hafida
    Boulmerka, Aissa
    Bellour, Azzeddine
    Birem, Fouzia
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 417
12345