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      Jacobi-Predictor-Corrector Approach for the Fractional Ordinary Differential Equations

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          Abstract

          We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t. the Jacobi-weight function \(\omega(s)=(1-s)^{\alpha-1}(1+s)^0\). This method has the computational cost O(N) and the convergent order \(IN\), where \(N\) and \(IN\) are, respectively, the total computational steps and the number of used interpolating points. The detailed error analysis is performed, and the extensive numerical experiments confirm the theoretical results and show the robustness of this method.

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          Numerical algorithm for the time fractional Fokker–Planck equation

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            Analysis of a system of fractional differential equations

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              Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces

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                Author and article information

                Journal
                28 January 2012
                2012-02-25
                Article
                10.1007/s10444-013-9302-7
                1201.5952
                506e78e7-13a7-4d8c-bf15-55ed5f531797

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                65M06, 65M12, 82C99
                Advances in Computational Mathematics, 40(1), 137-165, 2014
                24 pages, 5 figures
                math.NA

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