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Fractional Calculus and Applied Analysis

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Volume 18, Issue 3


High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II)

Jianxiong Cao / Changpin Li / YangQuan Chen
Published Online: 2015-05-23 | DOI: https://doi.org/10.1515/fca-2015-0045


In this paper, we first establish a high-order numerical algorithm for α-th (0 < α < 1) order Caputo derivative of a given function f(t), where the convergence rate is (4 − α)-th order. Then by using this new formula, an improved difference scheme with high order accuracy in time to solve Caputo-type fractional advection-diffusion equation with Dirichlet boundary conditions is constructed. Finally, numerical examples are carried out to confirm the efficiency of the constructed algorithm.

Keywords : Caputo derivative; advection-diffusion equation; difference scheme; stability; convergence


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About the article

Received: 2014-12-01

Published Online: 2015-05-23

Published in Print: 2015-06-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 3, Pages 735–761, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2015-0045.

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