几种米塔-列夫勒函数的数值算法的实现及其比较  

IMPLEMENTATION AND COMPARISON OF NUMERICAL ALGORITHMS FOR SEVERAL MITTAG-LEFFLER FUNCTIONS

作　　者：方宇孟 余波 袁晓[1] 谢雨婧[1] Fang Yumeng;Yu Bo;Yuan Xiao;Xie Yujing(College of Electronics and Information Engineering,Sichuan University,Chengdu 610065,Sichuan,China;College of Computer Science,Sichuan University,Chengdu 610065,Sichuan,China;School of Physics and Engineering Technology,Chengdu Normal University,Chengdu 611130,Sichuan,China)

机构地区：[1]四川大学电子信息学院,四川成都610065 [2]四川大学计算机学院,四川成都610065 [3]成都师范学院物理与工程技术学院,四川成都611130

出　　处：《计算机应用与软件》2024年第12期229-239,246,共12页Computer Applications and Software

基　　金：国家自然科学基金项目(U1730141)。

摘　　要：针对米塔-列夫勒函数类的表示、快速有效高精度计算、显示的问题,考察和实现四种数值算法:累加算法、分区算法、最优抛物线围线算法和帕德逼近算法。通过MATLAB软件编程和仿真,绘制、显示米塔-列夫勒函数,分析对比算法性能。实验结果表明,最优抛物线围线算法的计算精度和适用性最好,帕德逼近算法计算速度最快,分区算法优于累加算法。In order to explore the representation,fast and effective high precision calculation,display and application of mittag-leffler functions,we investigate and implement the four numerical algorithms:the accumulative algorithm,the partitioning algorithm,the optimal parabolic contour algorithm,and the Padéapproximation algorithm.Through MATLAB software programming and simulation,the mittag-leffler functions were drawn and displayed,and the performance of four algorithms was analyzed and compared.The experimental results show that the optimal parabolic contour algorithm has the best accuracy and applicability,the Padéapproximation algorithm has the fastest calculation speed,and the partitioning algorithm is superior to the accumulative algorithm.

关 键 词：分数微积分 特殊函数 围线积分 近似算法 分数阶信号分析 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O173.1[自动化与计算机技术—计算机科学与技术]