Optimal Petrov–Galerkin Spectral Approximation Method for the Fractional Diffusion, Advection, Reaction Equation on a Bounded Interval

Author:

Zheng Xiangcheng,Ervin V. J.ORCID,Wang Hong

Funder

Army Research Office

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference44 articles.

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2. Acosta, G., Borthagaray, J.P., Bruno, O., Maas, M.: Regularity theory and high order numerical methods for the (1-d)-fractional Laplacian. Math. Comput. 87, 1821–1857 (2018)

3. Babuška, I., Guo, B.: Direct and inverse approximation theorems for the $$p$$-version of the finite element method in the framework of weighted Besov spaces. I. Approximability of functions in the weighted Besov spaces. SIAM J. Numer. Anal. 39(5):1512–1538 (2001/02)

4. Benson, D.A., Wheatcraft, S.W., Meerschaert, M.M.: The fractional-order governing equation of Lévy motion. Water Resour. Res. 36(6), 1413–1424 (2000)

5. Bernardi, C., Dauge, M., Maday, Y.: Polynomials in the Sobolev World. Preprint IRMAR 07-14, Université de Rennes 1 (2007)

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