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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.

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
65T60 Numerical methods for wavelets
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References:

[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)
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