利用Block-Pulse函数求解分数阶泊松方程数值解  

The Fractional Order is Solved Using the Block-Pulse Function Poisson Equation Numerical Solution

作　　者：赵绚 朱帅 朱世昕[3] 杨泽民[4] ZHAO Xuan;ZHU Shuai;ZHU Shi-xin;YANG Ze-min(Yuncheng Advanced Normal College,Yuncheng 044000,China;School of Mathematics and Statistics,Shanxi Datong University,Datong 037009 China;School of Journalism and Communication,Shanxi Datong University,Datong 037009,China;School of Computer and Network Engineering,Shanxi Datong University,Datong 037009,China)

机构地区：[1]运城师范高等专科学校数学与计算机系,山西运城044000 [2]山西大同大学数学与统计学院,山西大同037009 [3]山西大同大学新闻与传媒学院,山西大同037009 [4]山西大同大学计算机与网络工程学院,山西大同037009

出　　处：《数学的实践与认识》2023年第4期231-237,共7页Mathematics in Practice and Theory

基　　金：山西省高等学校科技创新计划项目(2019L0774);山西省自然科学基金(201901D111305)。

摘　　要：借助于二维Block-Pulse函数求解分数阶泊松方程的数值解,并讨论了Dirichlet边界条件,方法是基于Block-Pulse函数的定义及性质,并结合相应的分数阶微分算子矩阵将原问题转化为含有未知变量的代数方程组,进而离散未知变量,求得原问题的数值解.而且还对所提方法进行了误差分析,最后给出的数值算例也验证了所提算法的有效性及可行性.This paper aims to numerically solve fractional-order Poisson equations with Dirichlet boundary conditions via Block-Pulse functions,this method is based on the definition and properties of Block-Pulse functions combined with their operational matrix of fractional differentiation.Then the original problem is transformed into a system of linear equations,the numerical solutions can be obtained by dispersing the unknown variables.Moreover the convergence analysis of the given method is investigated and the obtained numerical results show that our method is effective and practicable.

关 键 词：二维Block-Pulse函数 泊松方程 数值解 算子矩阵 分数阶 

分 类 号：O241.82[理学—计算数学]