几种分数阶微分数值解法的比较研究

Research on Comparing Several Numerical Solutions of Fractional-order Differential Methods

研究分数阶算法特性,基于抛物线插值方法,对分数阶微分计算设计了一种数值计算方法。明确了几种算法的特点,并进行了数值仿真,对于函数分数阶微分及分数阶微分方程的求解,在计算精度与计算时间开销方面,与迭代方法、线性插值方法进行了比较,结果表明迭代方法的计算精度和时间开销两方面都比较好,抛物线插值方法的计算精度高于线性插值,但线性插值在时间开销方面占优势,研究结果可为实际选择分数阶微分数值计算方法提供科学依据。

Based on the parabola interpolation,a novel method is designed to solve fractional-order differential systems numerically.We get the derivation of Gaussian function and the solution of the fractional-order differential by the numerical simulation.Three algorithms,i.e.iterative method,parabolic interpolation and linear interpolation,are compared on the aspects of time cost and precision of calculation.The results show that iterative method is better than others as to the time cost and precision of calculation.The precision of calculation of the parabolic interpolation method is higher than the linear interpolation,but the linear interpolation spends less time than the parabolic interpolation.The results are instructive to the actual choice of appropriate numerical method for calculation of fractional differential.