@inproceedings{d3be8f372aca4d3c8d014833953bf6b3,

title = "Numerical solutions of a class of nonlinear volterra integral equation",

abstract = "We consider numerical solutions of a class of nonlinear (nonstandard) Volterra integral equations. We first prove the existence and uniqueness of the solution of the Volterra integral equation in the context of the space of continuous funtions over a closed interval. We then use one point collocation methods and quadrature methods with a uniform mesh to construct solutions of the nonlinear VIE. We conclude that the repeated Simpson's rule gives better solutions when a reasonably large value of the stepsize is used.",

keywords = "Collocation methods, Nonstandard Volterra integral equations, Quadrature methods",

author = "Melusi Khumalo and Hlukaphi Mamba",

year = "2015",

language = "English",

series = "Lecture Notes in Engineering and Computer Science",

publisher = "Newswood Limited",

pages = "128--131",

editor = "Ao, {S. I.} and Len Gelman and Korsunsky, {Alexander M.} and Ao, {S. I.} and Hukins, {David W.L.} and Andrew Hunter and Ao, {S. I.} and Len Gelman",

booktitle = "WCE 2015 - World Congress on Engineering 2015",

note = "2015 World Congress on Engineering, WCE 2015 ; Conference date: 01-07-2015 Through 03-07-2015",

}