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Various wavelet methods for solving fractional Fredholm-Volterra integral equations. (English) Zbl 1319.65129

Li, Xing (ed.), Integral equations, boundary value problems and related problems. Selected papers of the 15th conference, Yínchuān, China, August 19–23, 2012. Dedicated to Chien-Ke Lu on the occasion of his 90th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4452-87-8/hbk; 978-981-4452-89-2/ebook). 275-285 (2013).
Summary: This paper presents the computational techniques for fractional Fredholm-Volterra integral equations. Various rationalized wavelet functions approximation together with collocation method is utilized to reduce this form of integral equation into a system of algebraic equations. Moreover, through illustrative example, a comparison of numerical solutions by using Haar wavelets, Legendre wavelets, Chebyshev wavelets, confirms the expected accuracy. Specially, this method is computationally attractive while the equations have not been solved analytically.
For the entire collection see [Zbl 1264.00037].

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
45D05 Volterra integral equations
45A05 Linear integral equations
26A33 Fractional derivatives and integrals
65T60 Numerical methods for wavelets
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