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Solving second kind integral equations with hybrid Fourier and block-pulse functions. (English) Zbl 1063.65144
Summary: We use a combination of Fourier and block-pulse functions on the interval [0,1], to solve the linear integral equation of the second kind. We convert the integral equation, to a system of linear equations. We show that our estimates have a good degree of accuracy.

MSC:
65R20Integral equations (numerical methods)
45B05Fredholm integral equations
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References:
[1] Kreyzing, E.: Introduction functional analysis with applications. (1978)
[2] K. Maleknejad, M.Tavassoli Kajani, Solving second kind integral equations by Galerkin methods with hybrid Legandre and block--pulse functions, Applied Mathematics and Computation 147 (2--3) 623--629 · Zbl 1101.65323
[3] K. Maleknejad, M.Tavassoli Kajani, Y. Mahmoudi, Numarical solution of linear Fredholm and Voltera integral equation of the second kind by using Legandre wavelets, Journal of Science, Islamic Republic of Iran 13 (2) 161--166
[4] Sweldens, W.; Piessens, R.: Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions. SIAM journal numerical analysis 31, 1240-1264 (1994) · Zbl 0822.65013
[5] Razzaghi, M.; Marzban, H. R.: Direct method for variational problems via hybrid of block-pulse and Chebyshev functions. Mathematical problems in engineering 6, 85-97 (2000) · Zbl 0987.65055