非线性弱奇性Volterra积分方程的谱配置法  

SPECTRAL COLLOCATION METHOD FOR NONLINEAR WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS

作　　者：古振东 Gu Zhendong(Guangdong University of Finance,Guangzhou 510521,China)

机构地区：[1]广东金融学院金融数学与统计学院,广州510521

出　　处：《计算数学》2021年第4期426-443,共18页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11971123);广东省自然科学基金(2017A030310636,2018A030313236);广东省高性能计算学会开放基金(2017060104);中山大学广东省计算科学重点实验室开放基金(2016001)资助。

摘　　要：基于已有文献的研究成果及前期工作,我们考察了非线性弱奇性Volterra积分方程(VIE)的谱配置法,并对该方法进行了收敛性分析.得到的结论是数值误差呈谱收敛.误差收敛阶与配置点个数及方程解的正则性相关.数值实验也证实了这一结论.本文的方法解决了已有文献中类似数值方法(Allaei(2016),Sohrabi(2017))存在的问题.Based onsome references and our previous works,we investigate the spectral collocation method for nonlinear weakly singular Volterra integral equations.The provided convergence analysis shows that the presented method has spectral convergence.The convergence orderrelates to the number of collocation points and the regularity of the solution to the equations.We carry out numerical experiments to confirm the theoretical results.The presented method is the improvement to the methods proposed by Allaei(2016)and Sohrabi(2017).

关 键 词：弱奇性Volterra积分方程 非线性 谱配置逼近 收敛性分析 

分 类 号：O175.5[理学—数学]