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The Finite Difference Methods for Fractional Ordinary Differential Equations
Authors:Changpin Li  Fanhai Zeng
Institution:1. Department of Mathematics , Shanghai University , Shanghai , P. R. China lcp@shu.edu.cn;3. Department of Mathematics , Shanghai University , Shanghai , P. R. China
Abstract:Fractional finite difference methods are useful to solve the fractional differential equations. The aim of this article is to 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 experiments are also presented, which verify the theoretical analysis.
Keywords:Caputo derivative  Convergence  Fractional Adams method  Fractional differential equations  Fractional Euler method  High order methods  Riemman–Liouville derivative  Stability
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