References
- K. Atkinson and J. Flores, The discrete collocation method for nonlinear integral equations, IMA J. Numer. Anal. 13 (1993), pp. 195–213. doi: 10.1093/imanum/13.2.195
- K.E. Atkinson and F.A. Potra, Projection and iterated projection methods for nonlinear integral equations, SIAM J. Numer. Anal. 24 (1987), pp. 1352–1373. doi: 10.1137/0724087
- E. Babolian and F. Fattahzadeh, Numerical solution of nonlinear of differential equations by using Chebyshev wavelet operational matrix of integration, Appl. Math. Comput. 188 (2007), pp. 417–426.
- E. Babolian and A. Shahsavaran, Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets, J. Comput. Appl. Math. 225 (2009), pp. 87–95. doi: 10.1016/j.cam.2008.07.003
- K. Bittner, Biorthogonal Wilson bases, Proc. SPIE Wavelet Applications in Signal and Image Processing VII, Vol. 3813, Denver, CO, USA, 1999, pp. 410–421.
- K. Bittner, Linear approximation and reproduction of polynomials by Wilson bases, J. Fourier Anal. Appl. 8 (2002), pp. 85–108. doi: 10.1007/s00041-002-0005-6
- H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge University Press, Cambridge, UK, 2004.
- C. Cattani and A. Kudreyko, Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kind, Appl. Math. Comput. 215 (2010), pp. 4164–4171.
- H.L. Dastjerdi and F.M.M. Ghain, The discrete collocation method for Fredholm–Hammerstien integral equations based on moving least squares method, Int. J. Comput. Math. 93 (2016), pp. 1347–1357. doi: 10.1080/00207160.2015.1046846
- I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
- I. Daubechies, S. Jaffard, and J.L. Journe, A simple Wilson orthonormal basis with exponential decay, SIAM J. Math. Anal. 22 (1991), pp. 554–573. doi: 10.1137/0522035
- H.G. Feichtinger and T. Strohmer (eds.), Advances in Gabor Analysis, Springer Science and Business Media, Davis, CA, 2012.
- D.F. Han and X.F. Shang, Numerical solution of integro-differential equations by using CAS wavelet operational matrix of integration, Appl. Math. Comput. 194 (2007), pp. 460–466.
- M.H. Heydari, M.R. Hooshmandasl, F.M.M. Ghaini, and F. Fereidouni, Two-dimensional Legendre wavelets for solving fractional Poisson equation with Dirichlet boundary conditions, Eng. Anal. Bound. Elem. 37 (2013), pp. 1331–1338. doi: 10.1016/j.enganabound.2013.07.002
- M.H. Heydari, M.R. Hooshmandasl, and F. Mohammadi, Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions, Appl. Math. Comput. 234 (2014), pp. 267–276.
- S.K. Kaushik and S. Panwar, An interplay between Gabor and Wilson frames, J. Funct. Space. Appl. 2013 (2013). doi: org/10.1155/2013/610917
- M.A. Krasnosel'skii and P.P. Zabareiko, Geometric Methods of Nonlinear Analysis, Springer-Verlag, Berlin Heidelberg, 1984.
- S. Kumar and I.H. Sloan, A new collocation-type method for Hammerstien integral equations, Math. Comput. 48 (1987), pp. 585–593. doi: 10.1090/S0025-5718-1987-0878692-4
- K. Maleknejad, H. Almasieh, and M. Roodaki, Triangular functions (TF) method for the solution of nonlinear Volterra–Fredholm integral equations, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), pp. 3293–3298. doi: 10.1016/j.cnsns.2009.12.015
- H. Saeedi, Application of Haar wavelets in solving nonlinear fractional Fredholm integro-differential equations, J. Maha. Math. Res. Cent. 2(1) (2013), pp. 15–28.
- H. Saeedi, On the linear B-spline scaling function operational matrix of fractional integration and its applications in solving fractional order differential equations, Iran. J. Sci. Technol. Trans. Sci. (2015), in press.
- H. Saeedi and F. Samimi, He's homotopy perturbation method for nonlinear Ferdholm integro-differential equations of fractional order, Int. J. Eng. Res. App. 2 (2012), pp. 52–56.
- F.G. Tricomi, Integral Equation, Dover, New York, 1982.
- G.M. Vainikko, Galerkin's perturbation method and the general theory of approximate methods for non-linear equations, USSR Comput. Math. Math. Phys. 7 (1967), pp. 1–41. doi: 10.1016/0041-5553(67)90140-1
- A.M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications, Springer-Verlag, Berlin, Heidelberg, 2011.
- S. Yousefi and A. Banifatemi, Numerical solution of Fredholm integral equations by using CAS wavelets, Appl. Math. Comput. 183 (2006), pp. 458–463.