Exponential Quadrature Rules for Linear Fractional Differential Equations

This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized Mittag–Leffler function. Then, suitable quadrature rules are dev...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 12; no. 1; pp. 219 - 244
Main Authors Garrappa, Roberto, Popolizio, Marina
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.02.2015
Subjects
Mathematics
Mathematics and Statistics
Fractional differential equation
quadrature rules
Primary 65L05
Secondary 26A33
linear problem
accuracy
Mittag–Leffler function
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ISSN1660-5446
1660-5454
DOI10.1007/s00009-014-0396-z

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Summary:This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized Mittag–Leffler function. Then, suitable quadrature rules are devised and order conditions of algebraic type are derived. Theoretical findings are validated by means of numerical experiments and the effectiveness of the proposed approach is illustrated by means of comparisons with other standard methods.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-014-0396-z