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Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via rationalized Haar functions. (English) Zbl 1102.65141
Summary: Rationalized Haar functions are developed to approximate of the nonlinear Volterra-Fredholm-Hammerstein integral equations. The properties of rationalized Haar functions are first presented, and the operational matrix of integration together with the product operational matrix are utilized to reduce the computation of integral equations into some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.

MSC:
65R20Integral equations (numerical methods)
45G10Nonsingular nonlinear integral equations
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References:
[1] Tricomi, F. G.: Integral equations. (1982)
[2] Lardy, L. J.: A variation of Nyström’s method for Hammerstein equations. J. integral equations 3, 123-129 (1982)
[3] Kumar, S.; Sloan, I. H.: A new collocation-type method for Hammerstein integral equations. J. math. Comput. 48, 123-129 (1987) · Zbl 0616.65142
[4] Brunner, H.: Implicitly linear collocation method for nonlinear Volterra equations. J. appl. Numer. math. 9, 235-247 (1982) · Zbl 0761.65103
[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] Hsiao, C. H.; Chen, C. F.: Solving integral equation via Walsh functions. Comput. electron. Eng. 6, 279-292 (1979) · Zbl 0431.45003
[7] Wang, C. H.; Shih, Y. P.: Explicit solutions of integral equations via block-pulse functions. Int. J. Syst. sci. 13, 773-782 (1982) · Zbl 0497.45010
[8] Hwang, C.; Shih, Y. P.: Solution of integral equations via Laguerre polynomials. Comput. electron. Eng. 9, 123-129 (1982) · Zbl 0503.65076
[9] Chang, R. Y.; Wang, M. L.: Solutions of integral equations via shifted Legendre polynomials. Int. J. Syst. sci. 16, 197-208 (1985) · Zbl 0577.65122
[10] Chou, J. H.; Horng, I. R.: Double shifted Chebyshev series for convolution integral and integral equations. Int. J. Contr. 42, 225-232 (1985) · Zbl 0566.93029
[11] Razzaghi, M.; Razzaghi, M.; Arabshahi, A.: Solution of convolution integral and Fredholm integral equations via double Fourier series. Appl. math. Comput. 40, 215-224 (1990) · Zbl 0717.65113
[12] Razzaghi, M.; Nazarzadeh, J.: Walsh functions. Wiley encycl. Electr. electron. Eng. 23, 429-440 (1999)
[13] K.G. Beauchamp, Walsh Functions, and Their Applications, 1975. · Zbl 0326.42007
[14] R.T. Lynch, J.J. Reis, Haar transform image coding, in: Proc. National Telecommun. Conf., Dallas, TX, 1976, pp. 44.3-1 -- 44.3-5.
[15] J.J. Reis, R.T. Lynch, J. Butman, Adaptive Haar transform video bandwidth reduction system for RPV’s, in: Proc. Ann. Meeting Soc. Photo Optic Inst. Eng. (SPIE), San Dieago, CA, 1976, pp. 24 -- 35.
[16] Ohkita, M.; Kobayashi, Y.: An application of rationalized Haar functions to solution of linear differential equations. IEEE trans. Circuit syst. 9, 853-862 (1986) · Zbl 0613.65072
[17] Ohkita, M.; Kobayashi, Y.: An application of rationalized Haar functions to solution of linear partial differential equations. Math. comput. Simulations 30, 419-428 (1988) · Zbl 0659.65109
[18] Yalcinbas, S.: Taylor polynomial solution of nonlinear Volterra -- Fredholm integral equations. Appl. math. Comput. 127, 195-206 (2002)
[19] Yousefi, S.; Razzaghi, M.: Legendre wavelets method for the nonlinear Volterra -- Fredholm integral equations. Math. comput. Simulation 70, 1-8 (2005) · Zbl 1205.65342
[20] Phillips, G. M.; Taylor, P. J.: Theory and application of numerical analysis. (1973) · Zbl 0312.65002
[21] Razzaghi, M.; Ordokhani, Y.: An application of rationalized Haar functions for variational problems. Appl. math. Comput. 122, 353-364 (2001) · Zbl 1020.49026