Comparison of numerical methods for fractional differential equations

By J. Connolly, Neville J. Ford. 2006

64 citations recorded by the source corpus.

In this paper we present a comparison of numerical methods for the solution of single term fractional differential equations. We review five available methods and use a graphical technique to compare their relative merits. We conclude by giving recommendations on the choice of efficient methods for any given single term fractional differential equation.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d5ece8a47d06431153a83360ecb166eea03a354d

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In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Explicit methods for fractional differential equations and their stability properties (2009, unknown): “This equation has been considered in several papers [2,3,8] for verifying convergence results and making comparison among different methods.”
Nonpolynomial collocation approximation of solutions to fractional differential equations (2013, background): “The theory and numerical analysis of fractional differential equations has also been widely developed in the last decades, see for example [4], [6], [7], [8], [10], [12], [14], [16], [18] and the references therein.”
A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations (2011, background): “[8] have reviewed some of the existing methods and explained their respective strengths and weaknesses.”
Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations (2009, unknown): “Furthermore, fractional multistep methods did not turn out to be the most efficient solvers for single term problems in our experiments in [15].”
A finite element method for time fractional partial differential equations (2011, methodology): “Numerical methods for fractional ordinary differential equations were studied in, for example, [6], [7], [8], [9] [12], [13].”