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Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration. (English) Zbl 1117.65178
Summary: We present the operational matrix of integration of a Chebyshev wavelets basis and the product operation matrix of it. Some comparative examples are included to demonstrate the superiority of operational matrix of Chebyshev wavelets to those of Legendre wavelets.

MSC:
65T60Wavelets (numerical methods)
65L05Initial value problems for ODE (numerical methods)
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References:
[1] Razzaghi, M.; Yousefi, S.: Legendre wavelets direct method for variational problems. Math. comput. Simul., 185-192 (2000)
[2] Hwang, C.; Shih, Y. P.: Laguerre series direct method for variational problems. J. optim. Theory appl. 39, 143-149 (1983) · Zbl 0481.49005
[3] Chang, R. Y.; Wang, M. L.: Shifted Legendre direct method for variational problems series. J. optim. Theory appl. 39, 299-307 (1983) · Zbl 0481.49004
[4] Horng, I. R.; Chou, J. H.: Shifted Chebyshev direct method for variational problems. Int. J. Syst. sci. 16, 855-861 (1985) · Zbl 0568.49019
[5] Razzaghi, M.; Razzaghi, M.: Fourier series direct method for variational problems. Int. J. Control 48, 887-895 (1988) · Zbl 0651.49012
[6] Chen, C. F.; Hsiao, C. H.: Haar wavelet method for solving lumped and distributed parameter systems. IEEE proc. Control theory appl. 144, 87-93 (1997) · Zbl 0880.93014
[7] Maleknejad, K.; Kajani, M. Tavassoli; Mahmoudi, Y.: Numerical solution of linear Fredholm and Volterra integral equation of the second kind by using Legendre wavelets, kybernetes. Int. J. Syst. math. 32, 1530-1539 (2003) · Zbl 1059.65127
[8] Razzaghi, M.; Yousefi, S.: Legendre wavelets operational matrix of integration. Int. J. Syst. sci. 32, No. 4, 495-502 (2001) · Zbl 1006.65151
[9] Daubechies, I.: Ten lectures on wavelets. (1992) · Zbl 0776.42018
[10] Fox, L.; Parker, I. B.: Chebyshev polynomials in numerical analysis. (1968) · Zbl 0153.17502