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Expansions on Quadrature Formulas and Numerical Solutions of Ordinary Differential Equations

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Recent Advances in Computational Optimization (WCO 2020)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 986))

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Abstract

This paper is a continuation of the discussion on optimization of the quadrature formulas and their applications in paper [6]. Second-order numerical solutions of Volterra integral equations are constructed using the quadrature formulas obtained in [6]. The numerical results presented in the paper confirm the effectiveness of the methods for numerical solution of ordinary differential equations.

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Acknowledgements

Venelin Todorov is supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICT in SES)”, contract No DO1-205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria and by the National Scientific Program for post doctoral and young scientists of Ministry of Education and Science 2020-2021. Yuri Dimitrov is supported by the Bulgarian National Science Fund under Young Scientists Project KP-06-M32/2 - 17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics”. The work is also supported by the Bulgarian National Fund of Science under Project DN 12/5-2017 “Efficient Stochastic Methods and Algorithms for Large-Scale Computational Problems” and by Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications” funded by National Science Fund - Bulgaria.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Department of Information Modeling, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str, Block 8, 1113, Sofia, Bulgaria

    Venelin Todorov, Yuri Dimitrov & Stoyan Poryazov

  2. Institute of Information and Communication Technologies, Department of Parallel Algorithms, Bulgarian Academy of Sciences, Acad. G. Bonchev Str, Block 25 A, 1113, Sofia, Bulgaria

    Venelin Todorov & Ivan Dimov

  3. University of Varna, Sofia, Bulgaria

    Radan Miryanov

  4. Department of Mathematics and Physics, University of Forestry, Sofia, Bulgaria

    Yuri Dimitrov

Authors
  1. Venelin Todorov
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  2. Yuri Dimitrov
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  3. Radan Miryanov
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  4. Ivan Dimov
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  5. Stoyan Poryazov
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Corresponding author

Correspondence to Venelin Todorov .

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Editors and Affiliations

  1. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Todorov, V., Dimitrov, Y., Miryanov, R., Dimov, I., Poryazov, S. (2022). Expansions on Quadrature Formulas and Numerical Solutions of Ordinary Differential Equations. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2020. Studies in Computational Intelligence, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-82397-9_25

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