Table of Contents
ISRN Applied Mathematics
Volume 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.

Linked References

  1. I. J. Schoenberg, “On trigonometric spline interpolation,” Journal of Mathematics and Mechanics, vol. 13, pp. 795–825, 1964. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. T. Lyche, L. L. Schumaker, and S. Stanley, “Quasi-interpolants based on trigonometric splines,” Journal of Approximation Theory, vol. 95, no. 2, pp. 280–309, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. T. Lyche and R. Winther, “A stable recurrence relation for trigonometric B-splines,” Journal of Approximation Theory, vol. 25, no. 3, pp. 266–279, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. Sharma and J. Tzimbalario, “A class of cardinal trigonometric splines,” SIAM Journal on Mathematical Analysis, vol. 7, no. 6, pp. 809–819, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. X. Liu, “Bivariate cardinal spline functions for digital signal processing,” in Trends in Approximation Theory, K. Kopotum, T. Lyche, and M. Neamtu, Eds., pp. 261–271, Vanderbilt University, Nashville, Tenn, USA, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. X. Liu, “Univariate and bivariate orthonormal splines and cardinal splines on compact supports,” Journal of Computational and Applied Mathematics, vol. 195, no. 1-2, pp. 93–105, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. X. Liu, “Interpolation by cardinal trigonometric splines,” International Journal of Pure and Applied Mathematics, vol. 40, no. 1, pp. 115–122, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. Kress, Linear Integral Equations, vol. 82 of Applied Mathematical Sciences, Springer, Berlin, Germany, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  9. B. L. Moiseiwitsch, Integral Equations, Dover, New York, NY, USA, 2005.
  10. A. D. Polyanin, Handbook of Integral Equations, CRC Press, Boca Raton, Fla, USA, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  11. A. Vahidian Kamyad, M. Mehrabinezhad, and J. Saberi-Nadjafi, “A numerical approach for solving linear and nonlinear volterra integral equations with controlled error,” IAENG International Journal of Applied Mathematics, vol. 40, no. 2, pp. 69–75, 2010. View at Google Scholar
  12. J. Goncerzewicz, H. Marcinkowska, W. Okrasiński, and K. Tabisz, “On the percolation of water from a cylindrical reservoir into the surrounding soil,” Zastosowania Matematyki, vol. 16, no. 2, pp. 249–261, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. D. Wei, “Uniqueness of solutions for a class of non-linear volterra integral equations without continuity,” Applied Mathematics and Mechanics, vol. 18, no. 12, pp. 1191–1196, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus