Short-term recursions for fractional differential equations

LIDIA ACETO; CECILIA MAGHERINI; Paolo Novati

doi:10.1063/1.4912305

Short-term recursions for fractional differential equations

LIDIA ACETO
, CECILIA MAGHERINI
, Paolo Novati

Department of Science and Technological Innovation

Research output: Contribution to conference › Paper › peer-review

Abstract

This paper deals with the numerical solution of Fractional Differential Equations by means of m-step recursions. For the construction of such formulas, we study a technique based on a rational approximation of the generating functions of Fractional Backward Differentiation Formulas (FBDFs). The so-defined methods simulate very well the properties of the underlying FBDFs with important computational advantages. This fact becomes particularly evident especially in the case when they are used for solving problems arising from the semi-discretization of fractional partial differential equations.

Original language	English
Pages	020001
DOIs	https://doi.org/10.1063/1.4912305
Publication status	Published - 2015
Event	International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rodi (Grecia) Duration: 1 Jan 2015 → …

Conference

Conference	International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
City	Rodi (Grecia)
Period	1/01/15 → …

Keywords

Fractional BDF
Fractional Differential Equations
Matrix functions

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10.1063/1.4912305

https://hdl.handle.net/11579/126244

Cite this

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title = "Short-term recursions for fractional differential equations",

abstract = "This paper deals with the numerical solution of Fractional Differential Equations by means of m-step recursions. For the construction of such formulas, we study a technique based on a rational approximation of the generating functions of Fractional Backward Differentiation Formulas (FBDFs). The so-defined methods simulate very well the properties of the underlying FBDFs with important computational advantages. This fact becomes particularly evident especially in the case when they are used for solving problems arising from the semi-discretization of fractional partial differential equations.",

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AU - MAGHERINI, CECILIA

AU - Novati, Paolo

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N2 - This paper deals with the numerical solution of Fractional Differential Equations by means of m-step recursions. For the construction of such formulas, we study a technique based on a rational approximation of the generating functions of Fractional Backward Differentiation Formulas (FBDFs). The so-defined methods simulate very well the properties of the underlying FBDFs with important computational advantages. This fact becomes particularly evident especially in the case when they are used for solving problems arising from the semi-discretization of fractional partial differential equations.

AB - This paper deals with the numerical solution of Fractional Differential Equations by means of m-step recursions. For the construction of such formulas, we study a technique based on a rational approximation of the generating functions of Fractional Backward Differentiation Formulas (FBDFs). The so-defined methods simulate very well the properties of the underlying FBDFs with important computational advantages. This fact becomes particularly evident especially in the case when they are used for solving problems arising from the semi-discretization of fractional partial differential equations.

KW - Fractional BDF

KW - Fractional Differential Equations

KW - Matrix functions

KW - Fractional BDF

KW - Fractional Differential Equations

KW - Matrix functions

UR - https://iris.uniupo.it/handle/11579/126244

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DO - 10.1063/1.4912305

M3 - Paper

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Y2 - 1 January 2015

ER -

Short-term recursions for fractional differential equations

Abstract

Conference

Keywords

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