Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations  

作　　者：Yin Yang Yanping Chen Yunqing Huang Wei Yang 

机构地区：[1]Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Xiangtan 411105,China [2]School ofMathematical Sciences,South China Normal University,Guangzhou 510631,China

出　　处：《Advances in Applied Mathematics and Mechanics》2015年第1期74-88,共15页应用数学与力学进展（英文）

基　　金：supported by National Science Foundation of China(11301446,11271145);Foundation for Talent Introduction of Guangdong Provincial University,Specialized Research Fund for the Doctoral Program of Higher Education(20114407110009);the Project of Department of Education of Guangdong Province(2012KJCX0036);China Postdoctoral Science FoundationGrant(2013M531789);Project of Scientific Research Fund ofHunan Provincial Science and Technology Department(2013RS4057);the Research Foundation of Hunan Provincial Education Department(13B116).

摘　　要：A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind.We provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-norm and L¥-norm will decay exponentially provided that the kernel function is sufficiently smooth.Numerical results are presented,which confirm the theoretical prediction of the exponential rate of convergence.

关 键 词：Spectral method NONLINEAR Volterra integral equations 

分 类 号：O17[理学—数学]