×

Wavelet Galerkin method for numerical solution of nonlinear integral equation. (English) Zbl 1082.65596

Summary: The continuous Legendre wavelets constructed on the interval [0, 1] are used to solve nonlinear Volterra and Fredholm integral equations of the second kind. The nonlinear part of the integral equation is approximated by Legendre wavelets, and the nonlinear integral equation is reduced to a system of nonlinear equations. Numerical examples illustrates the pertinent features of the method.

MSC:

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
65T60 Numerical methods for wavelets
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, PA, and ISBN 0-89871-274-2. QA403.3.D38 1992. LCCC No. 92-13201, 1992. · Zbl 0776.42018
[2] Delves, L.M.; Mohammed, J.L., Computational methods for integral equations, (1983), Cambridge University Press Oxford
[3] K. Maleknejad, M.T. Kajani, Y. Mahmoudi, Numerical solution of linear Fredholm and Volterra integral equation of the second kind by using Legendre wavelets, J. Kybernet., in press. · Zbl 1059.65127
[4] K. Maleknejad, Y. Mahmoudi, Numerical solution of high-order non-linear Volterra-Fredholm integro-differential equations, J. Appl. Math. and Comp., in press. · Zbl 1032.65144
[5] K. Maleknejad, H. Mesgarani, T. Nikazad, Wavelet Galerkin solution for Fredholm integral equation of the second kind, Int. J. Eng. Sci., in press.
[6] M. Razzaghi, S. Yousefi, The Legendre wavelets operational matrix of integration, Int. J. Syst. Sci., in press. · Zbl 1006.65151
[7] Razzaghi, M.; Yousefi, S., Legendre wavelets direct method for variational problems, Math. comput. simul., 53, 185-192, (2000)
[8] Sezer, M., Taylor polynomial solution of Volterra integral equations, Int. J. math. educ. sci. technol., 25, 5, 625, (1994) · Zbl 0823.45005
[9] Yalsinbas, S., Taylor polynimial solutions of nonlinear Volterra-Fredholm integral equations, Appl. math. comput., 127, 195-206, (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.