四川大学学报（自然科学版）2024，Vol.61Issue(2)：88-93,6.DOI:10.19907/j.0490-6756.2024.023003
G-L分数导数高阶逼近算法的鲁比希生成函数系数的求解
Solving the coefficients of Lubich generating function in the algorithm for G-L fractional derivative with high-order approximation
摘要
Abstract
Researching the approximation order of G-L fractional derivative,the numerical algorithm with high precision is introduced,and three methods are proposed to solve the coefficients of Lubich generating function with high-order approximation.From the point of view of signal processing,the analytical expression of the coefficients of Lubich generating function is derived strictly theoretically for the first time by using the Lagrange interpolation approximation method.A generating function of any order is constructed.Through the equivalence of different forms of generating function,the coefficients of generating function are solved by mathematical induction and matrix equation,and the correctness of the conclusion is verified.关键词
分数导数/高阶逼近/鲁比希生成函数/拉格朗日插值逼近/数值算法Key words
Fractional derivative/High-order approximation/Lubich generating function/Lagrange interpo-lation approximation/Numerical algorithm分类
信息技术与安全科学引用本文复制引用
杨紫怡,袁晓..G-L分数导数高阶逼近算法的鲁比希生成函数系数的求解[J].四川大学学报（自然科学版）,2024,61(2):88-93,6.基金项目
国家自然科学基金(62171303) （62171303）
