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Proceedings of the 16th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 25

Optimized stochastic approach for integral equations

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DOI: http://dx.doi.org/10.15439/2021F54

Citation: Proceedings of the 16th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 25, pages 239–242 ()

Full text

Abstract. An optimized stochastic approach for Fredholm integral equations of the second kind is presented and discussed in the present paper. Numerical examples and results are discussed and Monte Carlo algorithms with various initial and transition probabilities are compared.

References

  1. I. Dimov, Monte Carlo Methods for Applied Scientists, New Jersey, London, Singapore, World Scientific, 2008, 291p.
  2. R. Georgieva, PhD Thesis: Computational complexity of Monte Carlo algorithms for multidimensional integrals and integral equations, Sofia, 2003
  3. J.H. Curtiss. Monte Carlo Methods for The Iteration of Linear Operators. J. Math. Phys., 32 209–232, (1954).
  4. A. Doucet, A.M. Johansen, V.B. Tadic. On solving integral equations using Markov chain Monte Carlo methods. Applied Mathematics and Computations, 216 2869–2880, (2010).
  5. I. Sobol. Numerical methods Monte Carlo. Nauka, Moscow, 1973.
  6. Veleva, E., Georgiev, I. R., Zheleva, I., & Filipova, M. (2020, December). Markov chains modelling of particulate matter (PM10) air contamination in the city of Ruse, Bulgaria. In AIP Conference Proceedings (Vol. 2302, No. 1, p. 060018). AIP Publishing LLC.