A Multilevel Approach for Stability Conditions in Fractional Time Diffusion Problems

Autor:	I. K. Youssef, Adel Rashed A. Ali
Rok vydání:	2020
Předmět:	History Stability conditions Exact solutions in general relativity Consistency (statistics) Differential equation Finite difference Applied mathematics Constant function Stability (probability) Computer Science Applications Education Mathematics Fractional calculus
Zdroj:	Journal of Physics: Conference Series. 1591:012085
ISSN:	1742-6596 1742-6588
DOI:	10.1088/1742-6596/1591/1/012085
Popis:	The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which transmit the memory and hereditary effects to other terms is examined. The theoretical results is applied to a numerical example. The calculated solution has a good agreement with the exact solution.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0f533f836f735e924c52b8cc941ebabe https://doi.org/10.1088/1742-6596/1591/1/012085 Zobrazit plný text záznamu