A successive iterative approach for two dimensional nonlinear Volterra-Fredholm integral equations

Document Type : Research Article

Authors

School of Mathematics and Computer Science, Damghan University, Damghan, Iran.

Abstract

In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. Several examples are provided to demonstrate the effciency of the approach.

Keywords

References

1. Atkinson, K. and Han, W. Theoretical Numerical Analysis: A Functional Analysis Framework, Texts in Appl. Math. 39 (2005), Springer, New York, second edition, .
2. Avazzadeh, Z., Heydari, M. and Loghmani, G. B. A Comparison Between Solving Two Dimensional Integral Equations by the Traditional Collocation Method and Radial Basis Functions, Appl. Math. Sciences, 5(23) (2011) 1145 - 1152.
3. Babolian, E. and Jafari Shaerlar, A. Two Dimensional Block Pulse Functions and Application to Solve Volterra-Fredholm Integral Equations with Galerkin Method, Int. J. Contemp. Math. Sciences, 6(16) (2011) 763-770.
4. Badr, A. A. Block-by-Block Method for Solving Nonlinear Volterra Fredholm Integral Equation, Math. Problems in Engineering, Article ID 537909, doi:10.1155/2010/537909, (2010) 8 pages.
5. Borzabadi, A. H. and Fard, O. S. A numerical scheme for a class of nonlinear Fredholm integral equations of the second kind, Journal of Comput. and Appl. Math. 232 (2009) 449-454.
6. Brunner, H. On the numerical solution of nonlinear Volterra-Fredholm integral equation by collocation methods, SIAM J. Numer. Anal. 27(4) (1990) 987-1000.
7. Brunner, H. and Messina, H. Time-stepping methods for Volterra Fredholm integral equations, Rediconti di Mathematica, Serie VII, 23 (2003) 329-342.
8. Chan, R. and Ng, M. K. Conjugate gradient methods for Toeplitz systems, SIAM Review, 38 (1996) 427-482.
9. Cherruault, Y. and Saccomandi, G. Some, New results for convergent of Adomian’s method applied to integral equation, Math. Comput. Modelling, 16(2) (1992) 85-93.
10. Farengo, R., Lee, Y. C. and Guzdar, P. N. An electromagnetic integral equation: application to microtearing modes, Phys. Fluids, 26 (1983) 3515-3523.
11. Guoqiang, H. Asymptotic error expansion for the Nystrom method for a Volterra-Fredholm integral equations, J. Comput. Appl. Math. 59 (1995)49-59.
12. Hacia, L. On approximate solution for integral equations of mixed type, ZAMM Z. Angew. Math. Mech. 76 (1996) 415-416.
13. Han, G. Q. and Wang, R. F. Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations, J. Comput. and Appl. Math, 139 (2002) 49-63.
14. Jerri, A. J. Introduction to Integral Equations with Applications, John Wiley and Sons, INC, (1999).
15. Kauthen, P. J. Continous time collocation methods for Volterra-Fredholm integral equations, Numer. Math. 56 (1989) 409-424.
16. Kress, R. Linear Integral Equations, Springer-Verlag, New York, (1989).
17. Maleknejad, K. and Hadizadeh, M. A new computational method for Volterra-Fredholm integral equations, J. Comput. Math. Appl. 37(9) (1999)1-8.
18. Nadjafi, J. S., Samadi, O. N. and Tohidi, E. Numerical Solution of Two Dimensional Volterra Integral Equations by Spectral Galerkin Method, Journal of Appl. Math. and Bioinformatics, 1(2) (2011) 159-174.
19. Pachpatte, B. G. On a New Inequality Applicable to Certain Volterra Fredholm Type Sum-difference Equations, Tamsui Oxford Journal of Math ematical Sciences, 26(2) (2010) 173-184.
20. Rajan, D. and Chaudhuri, S. Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations, IEEE Transactions on Pattern Analysis and Machine Intelligence, 25 (2003)1102-1117.
21. Stoer, J. and Bulirsch, R. Introduction to Numerical Analysis, Speringer Verlage, New York, (1993).
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