Table of Contents
ISRN Applied Mathematics
Volume 2014 (2014), Article ID 213909, 7 pages
http://dx.doi.org/10.1155/2014/213909
Research Article

The Applications of Cardinal Trigonometric Splines in Solving Nonlinear Integral Equations

1Department of Mathematics and Physics, Hefei University, Hefei 230601, China
2Department of Mathematics and Physics, University of La Verne, La Verne, CA 91750, USA

Received 3 December 2013; Accepted 15 January 2014; Published 4 March 2014

Academic Editors: Y. M. Cheng and L. You

Copyright © 2014 Jin Xie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The cardinal trigonometric splines on small compact supports are employed to solve integral equations. The unknown function is expressed as a linear combination of cardinal trigonometric splines functions. Then a simple system of equations on the coefficients is deducted. When solving the Volterra integral equations, the system is triangular, so it is relatively straight forward to solve the nonlinear system of the coefficients and a good approximation of the original solution is obtained. The sufficient condition for the existence of the solution is discussed and the convergence rate is investigated.