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Zhao, Jingjun; Li, Yu; Xu, Yang

A kind of product integration scheme for solving fractional ordinary differential equations. (English) Zbl 1405.65180

Appl. Numer. Math. 136, 279-292 (2019).
Summary: In this paper, we construct a kind of product integration scheme for the nonlinear fractional ordinary differential equation. We design the scheme by considering the equivalent Volterra integral equation and using the idea of local Fourier expansion. We prove the high accuracy property of the new scheme and provide the stability analysis. Numerical experiments demonstrate the effectiveness of the scheme.

Cited in 7 Documents

MSC:

65R20 Numerical methods for integral equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A08 Fractional ordinary differential equations
45D05 Volterra integral equations

Keywords:

fractional differential equation; Caputo fractional derivative; local Fourier expansion; product integration
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References:

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