带线性延迟项的Volterra积分方程研究（英文）

发布时间：2018-03-23 13:15

  本文选题：Chebyshev谱配置方法　切入点：线性延迟项　出处：《湖南师范大学自然科学学报》2017年04期

【摘要】：本文主要研究带线性延迟项的Volterra型积分方程收敛情况.首先通过线性变换,我们将原先定义在[0,T]区间上带线性延迟项的Volterra型积分方程转换成定义在固定区间[-1,1]上的方程,然后利用Gauss积分公式求得近似解,进而再利用Chebyshev谱配置方法分析该方程的收敛性,最终借助格朗沃不等式及相关引理分析获得方程在L~∞和L_(ω~c)~2范数意义下呈现指数收敛的结论.最后给出数值例子,验证理论证明的结论.
[Abstract]:In this paper, we mainly study the convergence of Volterra type integral equations with linear delay terms. Firstly, by means of linear transformation, we transform the Volterra type integral equations with linear delay terms on [0T] interval into the equations defined on fixed interval [-1]. Then the approximate solution is obtained by using the Gauss integral formula, and then the convergence of the equation is analyzed by using the Chebyshev spectrum collocation method. Finally, the exponential convergence of the equation in the sense of L ~ 鈭，

本文编号：1653608