赖特函数的数值算法实现及其性能分析  

Numerical algorithm implementation and performance analysis of the Wright function

作　　者：李燕 袁晓[1] LI Yan;YUAN Xiao(College of Electronics and Information Engineering,Sichuan University,Chengdu 610065,China)

机构地区：[1]四川大学电子信息学院,成都610065

出　　处：《四川大学学报（自然科学版）》2024年第5期108-120,共13页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(62171303)。

摘　　要：针对赖特函数的快速有效高精度计算及显示的问题,研究并实现四种数值算法:累加算法、分区算法、拉式反演算法和超几何表示算法.利用MATLAB软件进行编程仿真,绘制、显示赖特函数图像,分析对比算法性能.实验结果表明,超几何表示算法的计算精度最好,分区算法的适用性最广,拉式反演算法和累加算法计算速度快.This study aims to investigate and implement four numerical algorithms,namely the accumulative algorithm,the partitioning algorithm,the Laplace inversion algorithm,and the hypergeometric representation algorithm.These algorithms are designed to explore fast and effective high precision arithmetic calculation and display of the Wright function.The Wright function is visualized and presented through MATLAB software programming and simulation,enabling the analysis and comparison of performance among four algorithms.The experimental results demonstrate that the hypergeometric representation algorithm exhibits superior computational accuracy,while the partition algorithm demonstrates extensive applicability.Additionally,both the Laplace inversion algorithm and the accumulation algorithm showcase remarkable computational speed.

关 键 词：分数微积分 特殊函数 算法分析 分区算法 MATLAB 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]