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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 652631, 8 pages
Numerical Solutions of a Class of Nonlinear Volterra Integral Equations
Department of Pure and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
Received 10 April 2014; Revised 17 June 2014; Accepted 26 June 2014; Published 9 July 2014
Academic Editor: Chun-Gang Zhu
Copyright © 2014 H. S. Malindzisa and M. Khumalo. 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.
- D. Saveljeva, “Quadratic and cubic spline collocation for Volterra integral equations,” 2006, http://dspace.utlib.ee/dspace/handle/10062/1163.
- B. G. Sloss and W. F. Blyth, “Corrington's Walsh function method applied to a nonlinear integral equation,” Journal of Integral Equations and Applications, vol. 6, no. 2, pp. 239–256, 1994.
- H. Brunner, “Iterated collocation methods for Volterra integral equations with delay arguments,” Mathematics of Computation, vol. 62, no. 206, pp. 581–599, 1994.
- J. G. Blom and H. Brunner, “The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods,” Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing, vol. 8, no. 5, pp. 806–830, 1987.
- T. Diogo, “Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations,” Journal of Computational and Applied Mathematics, vol. 229, no. 2, pp. 363–372, 2009.
- T. Diogo and P. Lima, “Collocation solutions of weakly singular Volterra integral equation,” Matemática Aplicada e Computacional, vol. 8, pp. 229–238, 2007.
- V. Horvat, “On collocation methods for Volterra integral equations with delay arguments,” Mathematical Communications, vol. 4, no. 1, pp. 93–109, 1999.
- R. Benitez and V. J. Bolos, “Blow-up collocation solutions of some Volterra integral equations,” 2011, http://arxiv.org/abs/1112.4658.
- M. Aigo, “On the numerical approximation of Volterra integral equations of the second kind using quadrature rules,” International Journal of Advanced Scientific and Technological Research, vol. 1, pp. 558–564, 2013.
- R. Katani and S. Shahmorad, “Block by block method for the systems of nonlinear Volterra integral equations,” Applied Mathematical Modelling, vol. 34, no. 2, pp. 400–406, 2010.
- F. Mirzaee, “A computational method for solving linear Volterra integral equations,” Applied Mathematical Sciences, vol. 6, no. 17–20, pp. 807–814, 2012.
- J. Saberi-Nadjafi and M. Heidari, “A quadrature method with variable step for solving linear Volterra integral equations of the second kind,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 549–554, 2007.
- H. Brunner, Collocation Methods For Volterra Integral And Related Functional Differential Equations, Cambridge University Press, Cambridge, Mass, 2004.
- H. Brunner, “Iterated collocation methods and their discretizations for Volterra integral equations,” SIAM Journal on Numerical Analysis, vol. 21, no. 6, pp. 1132–1145, 1984.
- M. S. Corrington, “Solution of differential and integral equations with walsh functions,” IEEE Trans Circuit Theory, vol. 20, no. 5, pp. 470–476, 1973.
- R. H. Rand, Lecture notes on nonlinear vibrations, 2003, http://www.math.cornell.edu/~rand/randdocs/nlvibe52.pdf.
- D. G. Zill, W. S. Wright, and M. R. Cullen, Differential Equations with Boundary Value Problems, Richard Stratton, 2012.