Nonpolynomial collocation approximation of solutions to fractional differential equations

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Abstract

We propose a non-polynomial collocation method for solving fractional di®erential equations. The construction of such a scheme is based on the classical equivalence between certain fractional di®erential equations and corresponding Volterra integral equations. Usually, we cannot expect the solution of a fractional di®erential equation to be smooth and this poses a challenge to the convergence analysis of numerical schemes. In this paper, the approach we present takes into account the potential non-regularity of the solution, and so we are able to obtain a result on optimal order of con- vergence without the need to impose inconvenient smoothness conditions on the solution. An error analysis is provided for the linear case and several examples are presented and discussed.
Original languageUnknown
Pages (from-to)874-891
JournalFractional Calculus and Applied Analysis
Volume16
Issue number4
DOIs
Publication statusPublished - 1 Jan 2013

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