On the rate of convergence of the Legendre spectral collocation method for multidimensional nonlinear Volterra-Fredholm integral equations  

作　　者：Nermeen A Elkot Mahmoud A Zaky Eid H Doha Ibrahem G Ameen 

机构地区：[1]Department of Mathematics,Faculty of Science,Cairo University,Giza 12613,Egypt [2]Department of Applied Mathematics,National Research Centre,Dokki,Cairo 12622,Egypt [3]Department of Mathematics,Faculty of Science,Al-Azhar University,Cairo,Egypt

出　　处：《Communications in Theoretical Physics》2021年第2期11-22,共12页理论物理通讯（英文版）

摘　　要：While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts exist.In this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation approach.Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view.Consequently,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors.The existence and uniqueness of the numerical solution are established.Numerical experiments are provided to support the theoretical convergence analysis.The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones.

关 键 词：spectral collocation method convergence analysis multi-dimensional integral equations 

分 类 号：O241.83[理学—计算数学]