About accuracy increase of fractional order derivative and integral computations by applying the Grunwald-Letnikov formula

作者：Brzezinski Dariusz W; Ostalczyk Piotr

来源：Communications in Nonlinear Science & Numerical Simulation, 2016, 40: 151-162.

DOI：10.1016/j.cnsns.2016.03.020

• Numerical methods
• Finite differences
• Fractional order derivatives and integrals
• Accuracy of numerical calculations
• Arbitrary precision

The aim of the paper is to gather and to survey various formulas for fractional order derivative and integral calculations according to their Grunwald-Letnikov definition. The paper presents evaluation results for some factors, which influence its accuracy and efficiency of computations: different formulas for the coefficients calculations, different forms of the formula and different schemas for the function discretization, including more points per step of summation. It also hints how to solve some of the serious programming issues when applying the formulas. The objective is to determine a recipe for the increase the default low computational accuracy and efficiency of this popular method of fractional order derivative and integral calculations.

• 出版日期2016-11