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The finite difference methods for fractional ordinary differential equations. (English) Zbl 1267.65094

The authors prove the stability and convergence of the fractional Euler method, the fractional Adams method, and the high-order methods based on the convolution formula by using the generalized discrete Gronwall inequality. Numerical examples are also presented.

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
34A08 Fractional ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations

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References:

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