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Jacobian-predictor-corrector approach for fractional differential equations. (English) Zbl 1322.65079

The authors deal with the solution of fractional ordinary differential equations. The presented solution approach is based on the application of Jacobi-Gauss-Lobatto quadrature rules applied to the integral equation formulation of the fractional differential equation. A detailed error analysis of the introduced numerical scheme is included.
The highest attainable order of convergence is the same as the number of backward grid points used in the underlying quadrature rule provided the right-hand side of the fractional equation is smooth enough. Finally, the presented numerical experiments confirm the theoretical results.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A08 Fractional ordinary differential equations
41A55 Approximate quadratures
65D05 Numerical interpolation
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

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References:

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