THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Yi Tian

MONTE CARLO METHOD WITH CONTROL VARIATE FOR INTEGRAL EQUATIONS

ABSTRACT
This paper combines the successive substitution method and Monte Carlo method with a control variate to solve Fredholm integral equations of the second kind. Some examples are gives to elucidate the solution process and the results reveal the efficiency of the method.
KEYWORDS
Monte Carlo method, control variate, Fredholm integral equation
PAPER SUBMITTED: 2017-02-20
PAPER REVISED: 2017-03-25
PAPER ACCEPTED: 2017-03-29
PUBLISHED ONLINE: 2018-09-10
DOI REFERENCE: https://doi.org/10.2298/TSCI1804765T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Issue 4, PAGES [1765 - 1771]
REFERENCES
  1. Liu, C. S., A New Method for Fredholm Integral Equations of 1-D Backward Heat Conduction Prob-lems, Computer Modeling in Engineering and Sciences, 47 (2009), 1, pp. 1-21
  2. Wang, Q. S., Wang, H. S., Meshless Method and Convergence Analysis for 2-Dimensional Fredholm In-tegral Equation with Complex Factors, Journal of Computational and Applied Mathematics, 304 (2016), Oct., pp. 18-25
  3. Bhrawy, A. H., et al., Legendre-Gauss-Lobatto Collocation Method for Solving Multi-Dimensional Fredholm Integral Equations, Computers and Mathematics with Applications, On-line first, doi.org/10.1016/j.camwa.2016.04.011
  4. Jin, C. M., Ding, J., Solving Fredholm Integral Equations via a Piecewise Linear Maximum Entropy Method, Journal of Computational and Applied Mathematics, 304 (2016), Oct., pp. 130-137
  5. Tian, Y., et al., A New Method for Solving a Class of Heat Conduction Equations, Thermal Science, 19 (2015), 4, pp. 1205-1210
  6. Tian, Y., Yan, Z. Z., Monte Carlo Method for Solving a Parabolic Problem, Thermal Science, 20 (2016), 3, pp. 933-937
  7. Farnoosh, R., Morteza, E., Monte Carlo Simulation for Solving Fredholm Integral Equations, Kyber-netes, 38 (2009), 9, pp. 1621-1629
  8. Yan, Z. Z., Hong, Z. M., Using the Monte Carlo Method to Solve Integral Equations Using a Modified Control Variate, Journal of Applied Mathematics and Computations, 242 (2014), Sept., pp. 764-777
  9. Wazwaz, A. M., Linear and Nonlinear Integral Equation: Methods and Application, Higher Education press, Beijing, 2011
PDF VERSION [DOWNLOAD]
Monte Carlo method with control variate for integral equations

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence