本文選題：Chebyshev譜配置方法　切入點：線性延遲項　出處：《湖南師范大學(xué)自然科學(xué)學(xué)報》2017年04期

【摘要】：本文主要研究帶線性延遲項的Volterra型積分方程收斂情況.首先通過線性變換,我們將原先定義在[0,T]區(qū)間上帶線性延遲項的Volterra型積分方程轉(zhuǎn)換成定義在固定區(qū)間[-1,1]上的方程,然后利用Gauss積分公式求得近似解,進而再利用Chebyshev譜配置方法分析該方程的收斂性,最終借助格朗沃不等式及相關(guān)引理分析獲得方程在L~∞和L_(ω~c)~2范數(shù)意義下呈現(xiàn)指數(shù)收斂的結(jié)論.最后給出數(shù)值例子,驗證理論證明的結(jié)論.
[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，

本文編號：1653608