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Keywords = semi-orthogonal B-spline wavelets

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15 pages, 330 KB  
Article
Quasilinearized Semi-Orthogonal B-Spline Wavelet Method for Solving Multi-Term Non-Linear Fractional Order Equations
by Can Liu, Xinming Zhang and Boying Wu
Mathematics 2020, 8(9), 1549; https://doi.org/10.3390/math8091549 - 10 Sep 2020
Cited by 1 | Viewed by 2155
Abstract
In the present article, we implement a new numerical scheme, the quasilinearized semi-orthogonal B-spline wavelet method, combining the semi-orthogonal B-spline wavelet collocation method with the quasilinearization method, for a class of multi-term non-linear fractional order equations that contain both the Riemann–Liouville fractional integral [...] Read more.
In the present article, we implement a new numerical scheme, the quasilinearized semi-orthogonal B-spline wavelet method, combining the semi-orthogonal B-spline wavelet collocation method with the quasilinearization method, for a class of multi-term non-linear fractional order equations that contain both the Riemann–Liouville fractional integral operator and the Caputo fractional differential operator. The quasilinearization method is utilized to convert the multi-term non-linear fractional order equation into a multi-term linear fractional order equation which, subsequently, is solved by means of semi-orthogonal B-spline wavelets. Herein, we investigate the operational matrix and the convergence of the proposed scheme. Several numerical results are delivered to confirm the accuracy and efficiency of our scheme. Full article
(This article belongs to the Special Issue Numerical Modeling and Analysis)
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