A collocation method for the numerical solution of nonlinear fractional dynamical systems
type: Item
instance of: scholarly article
title: A collocation method for the numerical solution of nonlinear fractional dynamical systems
zbMATH Open document ID: 1461.65224
published in: Algorithms
publication date: 2020-10-08T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 7257776
zbMATH Keywords: fractional differential equation
zbMATH Keywords: nonlinear dynamical system
zbMATH Keywords: B-spline
zbMATH Keywords: collocation method
author: Francesca Pitolli
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a12080156
OpenAlex ID: W2966647889
cites work: Q5190149
cites work: Applications of fractional calculus in physics
cites work: Q5699297
cites work: Fractional dynamics. Applications of fractional calculus to dynamics of particles, fields and media
cites work: Fractional calculus. Models and numerical methods
cites work: Fractional differentiation matrices with applications
cites work: Numerical methods for fractional partial differential equations
cites work: A fractional spline collocation-Galerkin method for the time-fractional diffusion equation
cites work: The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
cites work: Advances in Fractional Calculus
cites work: Q3141895
cites work: Q4250595
cites work: Smoothing transformation and spline collocation for nonlinear fractional initial and boundary value problems
cites work: Multidimensional weakly singular integral equations
cites work: Q3592409
cites work: Optimal B-spline bases for the numerical solution of fractional differential problems
cites work: Fractional Splines and Wavelets
cites work: Discrete Least Squares Approximations for Ordinary Differential Equations
cites work: Fractional dynamical system and its linearization theorem
cites work: Bayes Meets Krylov: Statistically Inspired Preconditioners for CGLS
cites work: Q3634482
DOI: 10.3390/A12080156
Recommended article: Application of the collocation method for solving nonlinear fractional integro-differential equations
Recommended article: Numerical approximation for a nonlinear variable-order fractional differential equation via a collocation method
Recommended article: Numerical solution of fractional integro-differential equations by collocation method
Recommended article: A Collocation Method for Solving Fractional Order Linear System
Recommended article: Nonpolynomial collocation approximation of solutions to fractional differential equations
Recommended article: Theoretical and computational analysis of nonlinear fractional integro-differential equations via collocation method
Recommended article: A collocation method in spline spaces for the solution of linear fractional dynamical systems
Recommended article: Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces
Recommended article: Q3412082
Recommended article: Q4975243
description: scientific article; zbMATH DE number 7257776