A Chebyshev approximation for solving nonlinear integral equations of Hammerstein type

Abstract 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 (FFT). The numerical examples and the number of operations show the advantages of this method to some other usual methods.

[1]  Handan Çerdik-Yaslan,et al.  An approximation method for the solution of nonlinear integral equations , 2006, Appl. Math. Comput..

[2]  Salih Yalçinbas.  Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations , 2002, Appl. Math. Comput..

[3]  Esmail Babolian,et al.  Numerical computation method in solving integral equations by using Chebyshev wavelet operational matrix of integration , 2007, Appl. Math. Comput..

[4]  Han Guo-qiang.  Asymptotic error expansion of a collocation-type method for Volterra-Hammerstein integral equations , 1993 .

[5]  Yadollah Ordokhani,et al.  Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via rationalized Haar functions , 2006, Appl. Math. Comput..

[6]  Ian H. Sloan,et al.  A new collocation-type method for Hammerstein integral equations , 1987 .

[7]  L. Delves,et al.  Computational methods for integral equations: Frontmatter , 1985 .

[8]  V. Hutson.  Integral Equations , 1967, Nature.

[9]  Mohsen Razzaghi,et al.  Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations , 2005, Math. Comput. Simul..

[10]  Ali Vahidian Kamyad,et al.  A different approach for solving the nonlinear Fredholm integral equations of the second kind , 2006, Appl. Math. Comput..

[11]  Esmail Babolian,et al.  Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration , 2007, Appl. Math. Comput..

[12]  Hermann Brunner,et al.  Implicitly linear collocation methods for nonlinear Volterra equations , 1992 .