A fast numerical method for fractional partial differential equations

Autor:	S. Mockary, E. Babolian, A. R. Vahidi
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	System of fractional differential equations Operational matrices Chebyshev polynomials Caputo-fractional derivative Fractional partial differential equations Mathematics QA1-939
Zdroj:	Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-20 (2019)
Druh dokumentu:	article
ISSN:	1687-1847
DOI:	10.1186/s13662-019-2390-z
Popis:	Abstract In this paper, we use operational matrices of Chebyshev polynomials to solve fractional partial differential equations (FPDEs). We approximate the second partial derivative of the solution of linear FPDEs by operational matrices of shifted Chebyshev polynomials. We apply the operational matrix of integration and fractional integration to obtain approximations of (fractional) partial derivatives of the solution and the approximation of the solution. Then we substitute the operational matrix approximations in the FPDEs to obtain a system of linear algebraic equations. Finally, solving this system, we obtain the approximate solution. Numerical experiments show an exponential rate of convergence and hence the efficiency and effectiveness of the method.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/02dce18656d0479eacb9f748592ba567 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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