High order numerical methods for fractional terminal value problems

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

In this paper we present a shooting algorithm to solve fractional terminal (or boundary) value problems. The convergence order of the numerical method we describe can be derived based upon properties of the equation being solved and we do not need to impose smoothness conditions on the solution for our analysis. The work is a sequel to our recent investigation where we constructed a nonpolynomial collocation method for the approximation of the solution to fractional initial value problems. Here we show that the method can be adapted for the effective approximation of the solution of terminal value problems. Moreover, we compare the efficiency of this numerical scheme against other existing methods.
Original languageUnknown
Pages (from-to)55-70
JournalComputational Methods In Applied Mathematics
Volume14
Issue number1
DOIs
Publication statusPublished - 1 Jan 2013

Cite this

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title = "High order numerical methods for fractional terminal value problems",
abstract = "In this paper we present a shooting algorithm to solve fractional terminal (or boundary) value problems. The convergence order of the numerical method we describe can be derived based upon properties of the equation being solved and we do not need to impose smoothness conditions on the solution for our analysis. The work is a sequel to our recent investigation where we constructed a nonpolynomial collocation method for the approximation of the solution to fractional initial value problems. Here we show that the method can be adapted for the effective approximation of the solution of terminal value problems. Moreover, we compare the efficiency of this numerical scheme against other existing methods.",
author = "Rebelo, {Magda Stela de Jesus}",
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High order numerical methods for fractional terminal value problems. / Rebelo, Magda Stela de Jesus.

In: Computational Methods In Applied Mathematics, Vol. 14, No. 1, 01.01.2013, p. 55-70.

Research output: Contribution to journalArticle

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AB - In this paper we present a shooting algorithm to solve fractional terminal (or boundary) value problems. The convergence order of the numerical method we describe can be derived based upon properties of the equation being solved and we do not need to impose smoothness conditions on the solution for our analysis. The work is a sequel to our recent investigation where we constructed a nonpolynomial collocation method for the approximation of the solution to fractional initial value problems. Here we show that the method can be adapted for the effective approximation of the solution of terminal value problems. Moreover, we compare the efficiency of this numerical scheme against other existing methods.

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