摘要
QBD方程在应用概率论、排队论和随机模拟等领域中具有广泛的应用.本文研究了QBD方程的数值解法,提出了一类预估校正法以求解方程,并给出了方法的收敛性分析.理论分析和数值例子表明本文所提的方法是可行的,而且与已有的几类不动点迭代法相比也是较为有效的.
QBD equations are widely used in the fields of applied probability,queuing theory,stochastic simulation and etc.In this paper,numerical solution of QBD equations is studied.A class of predictive correction method is proposed to solve the equation,and the convergence analysis of the method is given.Theoretical analysis and numerical examples show that the proposed method is feasible and is more effective than existing fixed point iteration methods.
作者
赵晓潞
关晋瑞
付亚茹
ZHAO Xiaolu;GUAN Jinrui;FU Yaru(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030619,China)
出处
《应用数学》
北大核心
2025年第3期886-895,共10页
Mathematica Applicata
基金
国家自然科学基金(12001395)
山西省科技创新人才团队专项资助(202204051002018)
山西省回国留学人员科研资助项目(2022-169)
山西省基础研究计划项目(202203021212189)。
关键词
QBD方程
M-矩阵
最小非负解
不动点迭代法
预估校正法
QBD equation
M-matrix
Minimal nonnegative solution
Fixed point iteration method
Predictive correction method
