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

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

2012-01-28

arxiv.org/abs/1201.5952v2

Mathematics

Numerical Analysis

24 pages, 5 figures

Scientific paper

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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