Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces

M. Luísa Morgado; Magda Rebelo

doi:10.1007/978-3-030-56323-3_36

Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces

M. Luísa Morgado, Magda Rebelo

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, we develop an accurate collocation scheme for ordinary initial value problems of the Caputo type and in order to illustrate the performance of the method we provide several numerical examples. At the end, we also indicate how this method can be used to approximate the solution of time-fractional diffusion equations. At it will be seen, it allows us to obtain accurate solutions even when the solution is not smooth at the origin.

Original language	English
Title of host publication	Differential and Difference Equations with Applications, ICDDEA 2019
Editors	Sandra Pinelas, Sandra Pinelas, John R. Graef, Stefan Hilger, Peter Kloeden, Christos Schinas
Place of Publication	Cham
Publisher	Springer
Pages	467-479
Number of pages	13
ISBN (Electronic)	978-3-030-56323-3
ISBN (Print)	978-3-030-56322-6
DOIs	https://doi.org/10.1007/978-3-030-56323-3_36
Publication status	Published - 2020
Event	4th International Conference on Differential and Difference Equations with Applications, ICDDEA 2019 - Lisbon, Portugal Duration: 1 Jul 2019 → 5 Jul 2019

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Publisher	Springer
Volume	333
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	4th International Conference on Differential and Difference Equations with Applications, ICDDEA 2019
Country/Territory	Portugal
City	Lisbon
Period	1/07/19 → 5/07/19

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10.1007/978-3-030-56323-3_36

Cite this

Morgado, M. L., & Rebelo, M. (2020). Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces. In S. Pinelas, S. Pinelas, J. R. Graef, S. Hilger, P. Kloeden, & C. Schinas (Eds.), Differential and Difference Equations with Applications, ICDDEA 2019 (pp. 467-479). (Springer Proceedings in Mathematics and Statistics; Vol. 333). Springer. https://doi.org/10.1007/978-3-030-56323-3_36

Morgado, M. Luísa ; Rebelo, Magda. / Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces. Differential and Difference Equations with Applications, ICDDEA 2019. editor / Sandra Pinelas ; Sandra Pinelas ; John R. Graef ; Stefan Hilger ; Peter Kloeden ; Christos Schinas. Cham : Springer, 2020. pp. 467-479 (Springer Proceedings in Mathematics and Statistics).

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abstract = "In this paper, we develop an accurate collocation scheme for ordinary initial value problems of the Caputo type and in order to illustrate the performance of the method we provide several numerical examples. At the end, we also indicate how this method can be used to approximate the solution of time-fractional diffusion equations. At it will be seen, it allows us to obtain accurate solutions even when the solution is not smooth at the origin.",

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Morgado, ML & Rebelo, M 2020, Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces. in S Pinelas, S Pinelas, JR Graef, S Hilger, P Kloeden & C Schinas (eds), Differential and Difference Equations with Applications, ICDDEA 2019. Springer Proceedings in Mathematics and Statistics, vol. 333, Springer, Cham, pp. 467-479, 4th International Conference on Differential and Difference Equations with Applications, ICDDEA 2019, Lisbon, Portugal, 1/07/19. https://doi.org/10.1007/978-3-030-56323-3_36

Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces. / Morgado, M. Luísa; Rebelo, Magda.
Differential and Difference Equations with Applications, ICDDEA 2019. ed. / Sandra Pinelas; Sandra Pinelas; John R. Graef; Stefan Hilger; Peter Kloeden; Christos Schinas. Cham: Springer, 2020. p. 467-479 (Springer Proceedings in Mathematics and Statistics; Vol. 333).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Morgado ML, Rebelo M. Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces. In Pinelas S, Pinelas S, Graef JR, Hilger S, Kloeden P, Schinas C, editors, Differential and Difference Equations with Applications, ICDDEA 2019. Cham: Springer. 2020. p. 467-479. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-56323-3_36

Collocation Solution of Fractional Differential Equations in Piecewise Nonpolynomial Spaces

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