Computational method based on Bernstein operational matrices for nonlinear Volterra-Fredholm-Hammerstein integral equations

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 1, 2012, Pages 52-61

  Maleknejad, K ^a   Hashemizadeh, E ^a   Basirat, B ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Bernstein polynomial; Nonlinear integral equation; Operational matrix; Volterra Fredholm Hammerstein

Indexed keywords

MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; NUMERICAL METHODS; POLYNOMIALS;

BERNSTEIN POLYNOMIAL; FREDHOLM-HAMMERSTEIN; HAMMERSTEIN INTEGRAL EQUATIONS; NONLINEAR INTEGRAL EQUATIONS; OPERATIONAL MATRICES; OPERATIONAL MATRIX OF INTEGRATION; POLYNOMIAL MATRICES; PROPERTY; VOLTERRA-FREDHOLM; VOLTERRUM-FREDHOLM-HAMMERSTEIN;

INTEGRAL EQUATIONS;

EID: 79961027579     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.04.023     Document Type: Article

References (22)

1. Voitovich N.N., Reshnyak O.O. Solutions of nonlinear integral equation of synthesis of the linear antenna arrays. BSUAE J Appl Electron 1999, 2(1):43-52.
2. Jaswon M.A., Symm G.T. Integral equation methods in potential theory and elastostatics 1977, Academic Press, London.
3. Schiavane P., Constanda C., Mioduchowski A. Integral methods in science and engineering 2002, Birkhauser, Boston.
4. Abdou M.A. On asymptotic methods for Fredholm-Volterra integral equation of the second kind in contact problems. J Comput Appl Math 2003, 154:431-446.
5. Bloom F. Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory. J Math Anal Appl 1980, 73:524-542.
6. Jiang S., Rokhlin V. Second kind integral equations for the classical potential theory on open surface II. J Comput Phys 2004, 195:1-16.
7. Semetanian B.J. On an integral equation for axially symmetric problem in the case of an elastic body containing an inclusion. J Comput Appl Math 2007, 200:12-20.
8. Maleknejad K., Hashemizadeh E., Ezzati R. A new approach to the numerical solution of Volterra integral equations by using Bernsteins approximation. Commun Nonlinear Sci Numer Simulat 2011, 16:647-655.
9. Doha E.H., Bhrawy A.H., Saker M.A. Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations. Appl Math Lett 2011, 24:559-565.
10. Mandal B.N., Bhattacharya S. Numerical solution of some classes of integral equations using Bernstein polynomials. Appl Math Comput 2007, 190:1707-1716.
11. Rivlin T.J. An introduction to the approximation of functions 1969, Dover Publications, New York.
12. Yousefi S.A., Behroozifar M. Operational matrices of Bernstein polynomials and their applications. Int J Syst Sci 2010, 41(6):709-716.
13. Marzban H.R., Tabrizidooz H.R., Razzaghi M. A composite collocation method for the nonlinear mixed Volterra-Fredholm-Hammerstein integral equations. Commun Nonlinear Sci Numer Simulat 2011, 16:1186-1194.
14. Ordokhani Y. Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via rationalized Haar functions. Appl Math Comput 2006, 180:436-443.
15. Maleknejad K., Almasieh H., Roodaki M. Triangular functions (TF) method for the solution of nonlinear Volterra-Fredholm integral equations. Commun Nonlinear Sci Numer Simulat 2010, 15:3293-3298.
16. Mahmoudi Y. Taylor polynomial solution of non-linear Volterra-Fredholm integral equation. Int J Comput Math 2005, 82(7):881-887.
17. Kreyszig E. Introductory functional analysis with applications 1978, John Wiley and sons, New York.
18. Snyder M.A. Chebychev methods in numerical approximation 1996, Prentice-Hall, Englewood Clifs, NJ.
19. Golberg M.A., Chen C.S. Discrete projection methods for integral equations. Southampton: Comput Mech Publicat 1997, 178-306.
20. Kalman R.E., Kalaba R.E. Quasilinearization and nonlinear boundary-value problems 1969, Elsevier, New York.
21. Kumar S., Sloan I.H. A new collocation-type method for Hammerstein integral equations. J Math Comput 1987, 48:123-129.
22. Ordokhani Y., Razzaghi M. Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via a collocation method and rationalized Haar functions. Appl Math Lett 2008, 21:4-9.