Bernstein算子矩阵法求高阶弱奇异积分微分方程数值解  

Bernstein Operational Matrix Method for Solving the Numerical Solution of High Order Integro-Differential Equation with Weakly Singular

作　　者：单锐[1] 魏金侠[1] 张雁[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《华侨大学学报（自然科学版）》2012年第5期595-600,共6页Journal of Huaqiao University(Natural Science)

基　　金：河北省教育厅科学研究计划项目(2009159)

摘　　要：为了求高阶变系数且带有弱奇异积分核Volterra-Fredholm积分微分方程的数值解,提出了Bernstein算子矩阵法.利用Bernstein多项式的定义及其性质给出任意阶弱奇异积分的近似求积公式,同时也给出Bernstein多项式的微分算子矩阵.通过化简所求方程及离散化简后的方程,可将原问题转换为求代数方程组的解.最后,通过收敛性分析说明该方法是收敛的,并用数值算例验证了方法的有效性.In order to obtain the numerical solution for high order variable coefficients Volterra-Fredholm integro-differential equation with weakly singular kernels,we present a Bernstein operational matrix method in this paper.A approximate formula which solves solution for any arbitrary order weakly singular integral is given by using the definition of Bernstein polynomial and some properties,and a operational matrix of derivative of Bernstein polynomial is also obtained.By translating the original problem through simplifying and descreting the equation,the problem can be transferred into a system of algebraic equations.Convergence analysis shows that the method is convergent.The numerical example shows that the method is effective.

关 键 词：高阶变系数 弱奇异 积分微分方程 BERNSTEIN多项式 算子矩阵 数值解 

分 类 号：O241.8[理学—计算数学]