ArticleEntropy (Basel, Switzerland)2018
Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative.
Article in Entropy (Basel, Switzerland), 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method.Entropy (Basel, Switzerland) · 2019Article
- Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method.Entropy (Basel, Switzerland) · 2019Article
- Approximation to Hadamard Derivative via the Finite Part Integral.Entropy (Basel, Switzerland) · 2018Article
- Power Law Behaviour in Complex Systems.Entropy (Basel, Switzerland) · 2018Article
- Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative.Entropy (Basel, Switzerland) · 2018Article
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6 authors.
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Abstract
In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grünwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis.
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