Sinc Nyström method for a class of nonlinear Volterra integral equations of the first kind

Advances in Difference Equations

Changqing Wang¹  Jin Huang²  Yanying Ma²  Hu Li² 

[1] School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, P.R. China;School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, P.R. China

关键词: nonlinear Volterra integral equation;    Sinc Nyström method;    SE transformation;    DE transformation;   

DOI  :  10.1186/s13662-016-0849-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Two numerical methods are proposed to solve nonlinear Volterra integral equations of the first kind. By using variable transformations, the problem is converted into linear Volterra integral equations of the second kind. These methods are implemented by utilizing Sinc quadrature, and then the problem is reduced to linear algebraic system equations. We state error analysis for the proposed methods, which show that these methods obtain exponential convergence order. Numerical examples are presented to confirm the theoretical estimation and illustrate the effectiveness of the proposed methods.

【 授权许可】

CC BY