求解分数阶常微分方程的一个高阶数值逼近格式

A high order numerical approximate scheme for fractional ordinary differential equation

对于分数阶常微分方程,我们通过直接离散的方法构造了一个高阶数值逼近格式。该数值方法是对分数阶导数直接进行离散。在每个小区间上,利用二次拉格朗日插值来进行逼近,从而获得分数阶导数逼近的高阶数值格式。该数值格式的收敛阶为3-α阶,其中0<α<1是分数阶导数的阶数。一系列的数值试验验证了理论预测的正确性。

By directly discrete method,we constructed a high numerical approximate scheme for the fractional ordinary differential equation,which is directly discretized for the fractional derivative.In every subinterval,we used quadratic Lagrange interpolation to approximate the fractional derivative.The convergence order of the numerical scheme is 3-α,which is the order of fractional derivatives in the interval of 0<α<1.A series of numerical tests were carried out to support the theoretical predictions.