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A Randomized Quasi-Monte Carlo Algorithms for Some Boundary Value Problems

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

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Abstract

This work continues the study of stochastic algorithms for solving boundary value problems, which started in our previous papers. The Dirichlet problem for the Laplace equation are discussed. We compare Monte Carlo and randomized quasi-Monte Carlo versions of algorithms. We use the Halton random points constructed by the Cranley-Patterson method.

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References

  1. Sabelfeld, K.K.: Monte Carlo Methods in Boundary Value Problems. Springer, Heidelberg (1991)

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Acknowledgements

The research has been supported by the Russian Foundation for Basic Research, project No. 17-01-00267.

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Authors and Affiliations

  1. Vologda State University, Lenina, 15, Vologda, Russia

    Alexander S. Sipin

Authors
  1. Alexander S. Sipin
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Corresponding author

Correspondence to Alexander S. Sipin .

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Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Sipin, A.S. (2020). A Randomized Quasi-Monte Carlo Algorithms for Some Boundary Value Problems. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_2

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