Finite-Difference Methods for Fractional Differential Equations of Order 1/2
- 3 Downloads
In this work, we study approximations of solutions of fractional differential equations of order 1/2. We present a new method of approximation and obtain the order of convergence. The presentation is given within the abstract framework of a semidiscrete approximation scheme, which includes finite-element methods, finite-difference schemes, and projection methods.
Keywords and phrasesfractional Cauchy problem Banach space α-times resolution family discretization methods difference scheme error estimate
AMS Subject Classification45L05 65M12
Unable to display preview. Download preview PDF.
- 2.E. G. Bajlekova, Fractional evolution equations in Banach spaces, Ph.D. thesis, Eindhoven University of Technology (2001).Google Scholar
- 17.S. Piskarev, Differential Equations in Banach Spaces and Their Approximations [in Russian], Moscow (2005).Google Scholar
- 18.S. Piskarev, “Approximation of fractional equations in abstract spaces,” in: Proc. Int. Conf. “Differential Equations and Dynamical Systems,” July 8–12, Suzdal (2016), p. 273.Google Scholar
- 19.S. Piskarev, “Fractional equations and difference schemes,” in: Proc. Int. Conference “Computational Methods in Applied Mathematics,” July 31–August 6, 2016, Javaskyla, Finland (2016).Google Scholar
- 20.E. A. Polyanskii, The Method of Correction of Parabolic Equations in Nonhomogeneous Wave Guide [in Russian], Moscow, Nauka (1985).Google Scholar