Numerical solution of nonlinear two-dimensional integral equations using rationalized Haar functions

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 3, 2011, Pages 1164-1175

  Babolian, E ^a   Bazm, S ^a   Lima, P ^b  

^a KHARAZMI UNIVERSITY   (Iran)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Bivariate collocation method; Nonlinear integral equations; Rationalized Haar functions; Two dimensional integral equations

Indexed keywords

ALGEBRA; INTEGRAL EQUATIONS; NONLINEAR EQUATIONS;

BIVARIATE; BIVARIATE COLLOCATION METHOD; COLLOCATION METHOD; NEWTON-COTES; NONLINEAR INTEGRAL EQUATIONS; NUMERICAL SOLUTION; RATIONALIZED HAAR FUNCTIONS; SECOND KINDS; TWO-DIMENSIONAL; TWO-DIMENSIONAL INTEGRAL EQUATIONS;

NUMERICAL METHODS;

EID: 77957368231     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.05.029     Document Type: Article

References (24)

1. Delves L.M., Mohamed J.L. Computational methods for integral equations 1985, Cambridge University Press, Cambridge.
2. Atkinson K.E. An introduction to numerical analysis 1989, John Wiley & Sons. 2nd ed.
3. Brunner H. Collocation method for Volterra integral and related functional equations 2004, Cambridge University Press, Cambridge.
4. Brunner H., Kauthen J.-P. The numerical solution of two-dimensional Volterra integral equations by collocation and iterated collocation. IMA J Numer Anal 1989, 9:47-59.
5. Kauthen J.P. Continuous time collocation method for Volterra-Fredholm integral equations. Numer Math 1989, 56:409-424.
6. Brunner H. On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods. SIAM J Numer Anal 1990, 27(4):987-1000.
7. Han G.Q., Zhang L.Q. Asymptotic expansion for the trapezoidal Nystrom method of linear Volterra-Fredholm equations. J Comput Appl Math 1994, 51:339-348.
8. Han G.Q., Zhang L.Q. Asymptotic error expansion of two-dimensional Volterra integral equation by iterated collocation. Appl Math Comput 1994, 61:269-285.
9. Han G.Q., Hayami K., Sugihara K., Wang J. Extrapolation method of iterated collocation solution for two-dimensional non-linear Volterra integral equation. Appl Math Comput 2000, 112:49-61.
10. Han G.Q., Jiong W. Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations. J Comput Appl Math 2001, 134:259-268.
11. Han G.Q., Wang R. Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations. J Comput Appl Math 2002, 139:49-63.
12. Han G.Q., Wang R. The extrapolation method for two-dimensional Volterra integral equations based on the asymptotic expansion of iterated Galerkin solutions. J Integral Equ Appl 2001, 13(1):15-34.
13. Maleknejad K, Sohrabi S, Baranji B. Two-dimensional PCBFs: application to nonlinear Volterra integral equations. In: Proceedings of the world congress on engineering (WCE), vol II. July 1-3, 2009, London, UK.
14. Tari A., Shahmorad S. A computational method for solving two-dimensional linear Fredholm integral equations of the second kind. ANZIAM J 2008, 49(4):543-549.
15. Encyclopaedia of mathematics (an updated and annotated translation of the Soviet Mathematical Encyclopaedia). Dordrecht/Boston/London: Kluwer Academic Publishers; 1992.
16. Lynch RT, Reis JJ. Haar transform image coding. In: Proceedings of the conference on national telecommunication, Dallas, TX, 1976, pp. 44.3-1-3.
17. Ohkita M., Kobayashi Y. An application of rationalized Haar functions to solution of linear differential equations. IEEE Trans Circuit Syst 1986, 33(9):853-862.
18. Ohkita M., Kobayashi Y. Application of the Haar functions to the solution of differential equations. Math Comput Simul 1983, 25:31-38.
19. Ohkita M., Kobayashi Y. An application of rationalized Haar functions to solution of linear partial differential equations. Math Comput Simul 1988, 30:419-428.
20. Razzaghi M., Ordokhani Y. A rationalized Haar functions method for nonlinear Fredholm Hammerstein integral equations. Intern J Comput Math 2002, 79(3):333-343.
21. Razzaghi M., Nazarzadeh J. Walsh functions. Wiley Encycl Electr Electron Eng 1999, 23:429-440.
22. Hsiao C.H., Chen C.F. Haar wavelet method for solving lumped and distributed-parameter systems. IEE Proc Control Theory Appl 1997, 144:87-94.
23. Rao G.P. Piecewise constant orthogonal functions and their applications to system and control 1983, Springer, Berlin.
24. Brunner H., van der Houwen P.J. The numerical solution of Volterra equations 1986, North-Holland, Amsterdam.