Numerical solution of time fractional diffusion systems
By Kevin Burrage, A. Cardone, R. D'Ambrosio, B. Paternoster. 2017
56 citations recorded by the source corpus.
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.
Subfields: Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/2f88c660b924267e6926f6a836e883a5a8658202
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Citations in the corpus
- Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial (2018, methodology): “We must mention that several other approaches have been however discussed in the literature: see, for instance, the generalized Adams methods [10], extensions of the Runge-Kutta methods [11], generalized exponential integrators [12,13], spectral methods [14,15], spectral collocation methods [16], me”