zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

65R20Integral equations (numerical methods)
45G10Nonsingular nonlinear integral equations
Full Text: DOI
[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