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TitleHigh-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
Author(s)Ferrás, Luís Jorge Lima
Ford, Neville
Morgado, Maria Luisa
Rebelo, Magda
KeywordsFractional diffusion
Caputo derivative
Nonpolynomial collocation method
Polynomial collocation method
Method of lines
Issue date2021
JournalMathematics in Computer Science
CitationFerrás, L. L., Ford, N., Morgado, M. L., & Rebelo, M. (2020, January 16). High-Order Methods for Systems of Fractional Ordinary Differential Equations and Their Application to Time-Fractional Diffusion Equations. Mathematics in Computer Science. Springer Science and Business Media LLC.
Abstract(s)Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method and we illustrate its feasibility and accuracy through some numerical examples. Finally, we solve the time-fractional diffusion equation using a combination of the method of lines and the newly developed hybrid method.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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