Abstract
In this paper, a numerical method is presented for solving nonlinear Volterra–Fredholm–Hammerstein integral equations. The proposed method takes full advantage of Nyström method and Sinc quadrature. Nonlinear integral equations is converted into nonlinear algebraic system equations. Error estimation is derived which is shown to has an exponential order of convergence. The accuracy and effectiveness of the proposed method are illustrated by some numerical experiments.
This work was supported by the National Natural Science Foundation of China (11371079).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Yousefi S, Razzaghi M (2005) Legendre wavelets method for the nonlinear Volterra–Fredholm integral equations. Math Comput Simul 70:1–8
Ordokhani Y, Razzaghi M (2008) Solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via a collocation method and rationalized Haar functions. Appl Math Lett 21:4–9
Maleknejad K, Hashemizadeh E, Basirat B (2012) Computational method based on Bernstein operational matrices for nonlinear Volterra–Fredholm–Hammerstein integral equations. Commun Nonlinear Sci Numer Simul 17:52–61
Yalcinbas S (2002) Taylor polynomial solutions of nonlinear Volterra–Fredholm integral equations[J]. Appl Math Comput 127:195–206
Bildik N, Inc M (2007) Modified decomposition method for nonlinear Volterra–Fredholm integral equations. Chaos, Solitons Fractals 33:308–313
Mirzaee F, Hoseini AA (2013) Numerical solution of nonlinear Volterra–Fredholm integral equations using hybrid of block-pulse functions and Taylor series. Alex Eng J 52:551–555
Rashidinia J, Zarebnia M (2007) Convergence of approximate solution of system of Fredholm integral equations. J Math Anal Appl 333:1216–1227
Lund J (1983) Sinc function quadrature rules for the Fourier integral. Math Comput 41:103–113
Bialecki B (1989) A modified sinc quadrature rule for functions with poles near the arc of integration. BIT Numer Math 29:464–476
Kress R, Sloan IH, Stenger F (1997) A sinc quadrature method for the double-layer integral equation in planar domains with corners. University of New South Wales, School of Mathematics, Sydney
Lund J, Bowers KL (1992) Sinc methods for quadrature and differential equations. SIAM, Philadelphia
Okayama T, Matsuo T, Sugihara M (2011) Improvement of a Sinc-collocation method for Fredholm integral equations of the second kind. BIT Numer Math 51:339–366
Okayama T, Matsuo T, Sugihara M (2015) Theoretical analysis of Sinc-Nyström methods for Volterra integral equations. Math Comput 84:1189–1215
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Ma, Y., Huang, J., Wang, C. (2017). Numerical Solutions of Nonlinear Volterra–Fredholm–Hammerstein Integral Equations Using Sinc Nyström Method. In: Balas, V., Jain, L., Zhao, X. (eds) Information Technology and Intelligent Transportation Systems. Advances in Intelligent Systems and Computing, vol 455. Springer, Cham. https://doi.org/10.1007/978-3-319-38771-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-38771-0_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-38769-7
Online ISBN: 978-3-319-38771-0
eBook Packages: EngineeringEngineering (R0)