基于MATLAB的赖特函数分区算法研究及实现

Research and Implementation of the Partitioning Algorithm for the Wright Function Based on MATLAB

物理数学中的多数特殊函数可将复平面划分区域采用不同数值技术来计算。赖特函数在分数微积分及其工程应用中有着重要作用,作为一类新型特殊函数也可使用分区算法进行数值计算。通过研究赖特函数在大参数下的渐近展开式和公式中系数的计算方法,修正积分表达式及积分半径选择定理的错误,进一步改进完善复数域赖特函数的分区算法,并利用MATLAB软件进行编程仿真分析算法精度。实验结果表明,分区算法的适用性广,有良好逼近效果。

Most special functions in physical mathematics can be calculated by dividing the complex plane into different regions and using various numerical techniques.The Wright function plays an important role in fractional calculus and its engineering applications.And as a new type of special function,the Wright function can also be calculated using the partitioning algorithm.By studying the asymptotic expansion of the Wright function under large parameters and the calculation method of coefficients in the formula,correcting the errors in the integral expression and the integral radius selection theorem,the partitioning algorithm of the Wright function in the complex field has been further improved and perfected,and finally MATLAB software is used for programming simulation to analyze the accuracy of the algorithm.The experimental results show that the partitioning algorithm has wide applicability and good approximation effect.