Open AccessJournal Article
Numerical solution of time fractional diffusion systems
TLDR
In this article, a general class of diffusion problem is considered, where the standard time derivative is replaced by a fractional one, and a mixed method is proposed, which consists of a finite difference scheme through space and a spectral collocation method through time.Abstract:
In this paper a general class of diffusion problem is considered, where the standard time derivative is replaced by a fractional one. For the numerical solution, a mixed method is proposed, which consists of a finite difference scheme through space and a spectral collocation method through time. The spectral method considerably reduces the computational cost with respect to step-by-step methods to discretize the fractional derivative. Some classes of spectral bases are considered, which exhibit different convergence rates and some numerical results based on time diffusion reaction diffusion equations are given.read more
Citations
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Journal ArticleDOI
Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial
TL;DR: This paper presents a set of MATLAB routines specifically devised for solving three families of fractional-order problems: fractional differential equations (FDEs) (also for the non-scalar case), multi-order systems (MOSs) of FDEs and multi-term FDE
Journal ArticleDOI
On an accurate discretization of a variable-order fractional reaction-diffusion equation
TL;DR: The theoretical analysis and high-accuracy of the proposed method are verified, and Comparative results indicate that the accuracy of the new discretization technique is superior to the other methods available in the literature.
Journal ArticleDOI
Long-term analysis of stochastic θ-methods for damped stochastic oscillators
TL;DR: In this article, a prior analysis of the error in the correlation matrix allows to infer the long-time behaviour of stochastic θ-methods and their capability to reproduce the same long-term features of the continuous dynamics.
Journal ArticleDOI
Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review
TL;DR: Both exact and discretized one-step and multistep collocation methods are considered, and main convergence results are illustrated, making some comparisons in terms of accuracy and efficiency.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Journal ArticleDOI
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
Journal ArticleDOI
Fractional Brownian Motions, Fractional Noises and Applications
Book
Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
TL;DR: In this article, the authors present a method for computing fractional derivatives of the Fractional Calculus using the Laplace Transform Method and the Fourier Transformer Transform of fractional Derivatives.
Journal ArticleDOI
Solution of the matrix equation AX + XB = C [F4]
R. H. Bartels,G. W. Stewart +1 more
TL;DR: The algorithm is supplied as one file of BCD 80 character card images at 556 B.P.I., even parity, on seven ~rack tape, and the user sends a small tape (wt. less than 1 lb.) the algorithm will be copied on it and returned to him at a charge of $10.O0 (U.S.and Canada) or $18.00 (elsewhere).
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