Expansion method for linear integral equations by cardinal B-spline wavelet and Shannon wavelet as bases for obtain Galerkin system. (English) Zbl 1088.65117

Summary: We apply the B-spline and Shannon wavelets bases for approximating the solution of linear integral equations of the second kind, then by this wavelet bases we construct a Galerkin system, which is important the expansion methods in solving linear integral equations. At the end, for showing efficiency of this method, we use numerical examples.


65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
65T60 Numerical methods for wavelets
Full Text: DOI


[1] Burrus, G. S.; Gopinath, R. A.; Guo, H., Introduction to Wavelets and Wavelet Transform (1998), Prentice Hall
[2] Walter, G. G.; Shen, X., Wavelets and Other Orthogonal Systems (2001), Chapman and Hall/CRC · Zbl 1005.42018
[3] Resnikoff, H. L.; Wells, R. O., Wavelet Analysis (1998), Springer · Zbl 0922.42020
[4] Delves, L. M.; Mohamed, J. L., Computational Methods for Integral Equations (1988), Cambridge University Press · Zbl 0662.65111
[5] Maleknejad, K.; Rahbar, D., Numerical solution of Fredholm integral equation of the second kind by using B-spline function, Int. J. Eng. Sci., 13, 5, 9-17 (2000)
[6] Maleknejad, K.; Mirzaee, F., Using rationalized Haar wavelet for solving linear integral equations, Appl. Math. Comput., 162, 2, 579-587 (2005) · Zbl 1067.65150
[7] Maleknejad, K.; Mesgarani, H.; Nizad, T., Wavelet-Galerkin solution for Fredholm integral equation of the second kind, Int. J. Eng. Sci., 13, 5, 75-80 (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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.