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Numerical solution of linear Fredholm and Volterra integral equation of the second kind by using Legendre wavelets. (English) Zbl 1059.65127

Summary: Uses the continuous Legendre wavelets on the interval \([0,1)\) in the manner of M. Razzaghi and S. Yousefi [Math. Comput. Simulation 53, No. 3, 185–192 (2000); Int. J. Syst. Sci. 32, No. 4, 495–502 (2001; Zbl 1006.65151)], to solve the linear second kind integral equations. We use quadrature formula for the calculation of inner products of any functions, which are required in the approximation for the integral equations. Then, we reduced the integral equation to the solution of linear algebraic equations.

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
45D05 Volterra integral equations
65T60 Numerical methods for wavelets

Citations:

Zbl 1006.65151
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References:

[1] Daubechies, I. (1992), ”Ten lectures on wavelets”,SIAM, Philadelphia, PA and ISBN 0-89871-274-2. QA403.3.D38 1992. LCCC No. 92-13201. · Zbl 0776.42018 · doi:10.1137/1.9781611970104
[2] DOI: 10.1016/0045-7906(82)90018-0 · Zbl 0503.65076 · doi:10.1016/0045-7906(82)90018-0
[3] DOI: 10.1007/BF00934611 · Zbl 0481.49005 · doi:10.1007/BF00934611
[4] DOI: 10.1016/S0898-1221(99)00107-8 · Zbl 0940.65151 · doi:10.1016/S0898-1221(99)00107-8
[5] DOI: 10.1016/S0378-4754(00)00170-1 · doi:10.1016/S0378-4754(00)00170-1
[6] Razzaghi, M. and Yousefi, S. (2003), ”The Legendre wavelets operational matrix of integration”,International Journal of Systems Science. · Zbl 1006.65151
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