×

zbMATH — the first resource for mathematics

A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type. (English) Zbl 1122.65409
Summary: A numerical method for solving Fredholm-Volterra Hammerstein integral equations is presented. This method is based on replacement of the unknown function by truncated series of well known Chebyshev expansion of functions.The quadrature formula which we use to calculate integral terms can be estimated by fast Fourier transform. The numerical examples and the number of operations show the advantages of this method to some other usual methods.

MSC:
65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Tricomi, F.G., Integral equations, (1982), Dover
[2] Brunner, H., Implicity linear collocation method for nonlinear Volterra equations, J. appl. numer. math., 9, 235-247, (1982)
[3] L.J. Lardy, A variation of Nysrtom’s method for Hammerstein integral equations 3 (1982) 123-129.
[4] Kumar, S.; Sloan, I.H., A new collocation-type method for Hammerstein integral equations, J. math. comput., 48, 123-129, (1987)
[5] Guoqiang, H., Asymptotic error expansion variation of a collocation method for volterra – hammerstein equations, J. appl. numer. math., 13, 357-369, (1993) · Zbl 0799.65150
[6] Ordokhani, Y., Solution of nonlinear volterra – fredholm – hammerstein integral equations via rationalized Haar functions, Appl. math. comput., 180, 436-443, (2006) · Zbl 1102.65141
[7] Yousefi, S.; Razzaghi, M., Legendre wavelet method for the nonlinear volterra – fredholm integral equations, Math. comp. simul., 70, 1-8, (2005) · Zbl 1205.65342
[8] Yashilbas, S., Taylor polynomial solution of nonlinear volterra – fredholm integral equations, Appl. math. comput., 127, 195-206, (2002)
[9] Akyuz-Dascioglu, A.; Cerdik Yaslan, H., An approximation method for the solution of nonlinear integral equations, Appl. math. comput., 174, 619-629, (2006) · Zbl 1089.65134
[10] Borzabadi, A.K.; Kamyad, A.V.; Mehne, H.H., A different approach for solving the nonlinear Fredholm integral equations of the second kind, Appl. math. comput., 173, 724-735, (2006) · Zbl 1092.65117
[11] E. Babolian, F. Fattahzadeh, Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.10.008. · Zbl 1117.65178
[12] E. Babolian, F. Fattahzadeh, Numerical Computation method in solving integral equations by using Chebyshev wavelet operational matrix of integration, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.10.073. · Zbl 1114.65366
[13] Delves, L.M.; Mohamad, J.L., Computational methods for integral equations, (1985), Cambridge University Press · Zbl 0592.65093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.