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Constructions of Second Order Approximations of the Caputo Fractional Derivative

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Large-Scale Scientific Computing (LSSC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13127))

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Abstract

In the present paper we study the properties of the weights of approximations of the second derivative and the Caputo fractional derivative. The approximations of the Caputo derivative are obtained by approximating the second derivative in the expansion formula of the L1 approximation. We show that the properties of their weights are similar to the properties of the weights of the L1 approximation of the Caputo derivative when a suitable choice of the parameters of the approximations is used. The experimental results of applications of the approximations for numerical solution of the two-term ordinary fractional differential equation are given in the paper.

The authors are supported by the Bulgarian National Science Fund under Young Scientists Project KP-06-M32/2 - 17.12.2019. Venelin Todorov is also supported by project No DO1-205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Sofia University, 1164, Sofia, Bulgaria

    Stoyan Apostolov

  2. Department of Mathematics and Physics, University of Forestry, 1756, Sofia, Bulgaria

    Yuri Dimitrov

  3. Department of Information Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Yuri Dimitrov & Venelin Todorov

  4. Department of Parallel Algorithms, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Venelin Todorov

Authors
  1. Stoyan Apostolov
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  2. Yuri Dimitrov
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  3. Venelin Todorov
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Corresponding author

Correspondence to Yuri Dimitrov .

Editor information

Editors and Affiliations

  1. IICT-BAS, Sofia, Bulgaria

    Ivan Lirkov

  2. IICT-BAS, Sofia, Bulgaria

    Svetozar Margenov

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Apostolov, S., Dimitrov, Y., Todorov, V. (2022). Constructions of Second Order Approximations of the Caputo Fractional Derivative. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2021. Lecture Notes in Computer Science, vol 13127. Springer, Cham. https://doi.org/10.1007/978-3-030-97549-4_3

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  • DOI: https://doi.org/10.1007/978-3-030-97549-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-97548-7

  • Online ISBN: 978-3-030-97549-4

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