Skip to main content
Springer Nature Link
Log in

An Improved Algorithm for Fredholm Integral Equations

  • Conference paper
  • First Online:
Large-Scale Scientific Computations (LSSC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13952))

Included in the following conference series:

  • 390 Accesses

Abstract

Integral equations are of high applicability in different areas of applied mathematics, physics, engineering, geophysics, electricity and magnetism, kinetic theory of gases, quantum mechanics, mathematical economics, and queuing theory. That is why it is reasonable to develop and study efficient and reliable approaches to solve integral equations. For multidimensional problems the existing biased stochastic algorithms based on evaluation of finite number of integrals will suffer more from the effect of high dimensionality, because they are based on quadrature points. So we need advanced unbiased algorithms for solving the multidimensional problem which will be developed in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Curtiss, J.H.: Monte Carlo methods for the iteration of linear operators. J. Math. Phys. 32, 209–232 (1954)

    Article  MathSciNet  Google Scholar 

  2. Dimov, I.T.: Monte Carlo Methods for Applied Scientists, p. 291. World Scientific, London (2008). ISBN: 10 981-02-2329-3

    Google Scholar 

  3. Dimov, I.T., Maire, S.: A new unbiased stochastic algorithm for solving linear Fredholm equations of the second kind. Adv. Comput. Math. 45, 1499–1519 (2019)

    Article  MathSciNet  Google Scholar 

  4. Dimov, I.T., Maire, S., Sellier, J.M.: A new Walk on Equations Monte Carlo method for solving systems of linear algebraic equations. Appl. Math. Model. 39(15), 4494–4510 (2014). https://doi.org/10.1016/j.apm.2014.12.018

    Article  MathSciNet  Google Scholar 

  5. Farnoosh, R., Ebrahimi, M.: Monte Carlo method for solving Fredholm integral equations of the second kind. Appl. Math. Comput. 195, 309–315 (2008)

    MathSciNet  Google Scholar 

  6. Kalos, M.H., Whitlock, P.A.: Monte Carlo Methods. Wiley-VCH (2008). ISBN: 978-3-527-40760-6

    Google Scholar 

Download references

Acknowledgements

Slavi Georgiev is supported by the Bulgarian National Science Fund (BNSF) under Project KP-06-M62/1 “Numerical deterministic, stochastic, machine and deep learning methods with applications in computational, quantitative, algorithmic finance, biomathematics, ecology and algebra” from 2022. Venelin Todorov is supported by BNSF under Project KP-06-N52/5 “Efficient methods for modeling, optimization and decision making” and BNSF under Project KP-06-N62/6 “Machine learning through physics-informed neural networks”. The work is also supported by BNSF under Bilateral Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications”.

Author information

Authors and Affiliations

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

    Venelin Todorov & Slavi Georgiev

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

    Venelin Todorov & Ivan Dimov

  3. Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, Angel Kanchev University of Ruse, 8 Studentska Str., 7004, Ruse, Bulgaria

    Slavi Georgiev

  4. Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria

    Stoyan Apostolov

Authors
  1. Venelin Todorov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Slavi Georgiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stoyan Apostolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ivan Dimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Venelin Todorov .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute of Information and Communication Technologies, Sofia, Bulgaria

    Svetozar Margenov

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Todorov, V., Georgiev, S., Apostolov, S., Dimov, I. (2024). An Improved Algorithm for Fredholm Integral Equations. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computations. LSSC 2023. Lecture Notes in Computer Science, vol 13952. Springer, Cham. https://doi.org/10.1007/978-3-031-56208-2_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-56208-2_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-56207-5

  • Online ISBN: 978-3-031-56208-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics