利用Caputo导数的性质和求解普通积分方程的Admas技巧,得到一种求解一类分数阶微分方程初值问题的显式方法;证明了其整体误差估计为O(h^θ),θ=min{α,2},并进行了稳定性分析。该方法在α〉1时比已有的几种显式方法具有更高的数值精度和收敛阶。
According to properties of the Caputo derivative and the Admas technique for ordinary integral equations, an explicit numerical scheme for the initial value problems of a class of fractional differential equations was obtained; and its global error was estimated to be O(h^θ),θ = min{a,2}, and the stability properties were considered. The method can provide higher precision and convergence order than the existing explicit numerical schemes when a 〉 1.