THERMAL SCIENCE

International Scientific Journal

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Yi Tian

,

Zai-Zai Yan

MONTE CARLO METHOD FOR SOLVING A PARABOLIC PROBLEM

ABSTRACT
In this paper, we present a numerical method based on random sampling for a parabolic problem. This method combines use of the Crank-Nicolson method and Monte Carlo method. In the numerical algorithm, we first discretize governing equations by Crank-Nicolson method, and obtain a large sparse system of linear algebraic equations, then use Monte Carlo method to solve the linear algebraic equations. To illustrate the usefulness of this technique, we apply it to some test problems.
KEYWORDS
Monte Carlo method, Crank-Nicolson method, system of linear algebraic equations
PAPER SUBMITTED: 2015-11-09
PAPER REVISED: 2016-02-05
PAPER ACCEPTED: 2016-02-05
PUBLISHED ONLINE: 2016-08-13
DOI REFERENCE: https://doi.org/10.2298/TSCI1603933T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 3, PAGES [933 - 937]
REFERENCES
  1. Tian, Y., et al., A New Method for Solving a Class of Heat Conduction Equation, Thermal Science, 19 (2015), 4, pp. 1205-1210
  2. Jia, Z. J., et al., Variational Principle for Unsteady Heat Conduction Equation, Thermal Science, 18 (2014), 3, pp. 1045-1047
  3. Liu, F. J., et al., He's Fractional Derivative for Heat Conduction in a Fractal Medium Arising in Silkworm Cocoon Hierarchy, Thermal Science, 19 (2015), 4, pp. 1155-1159
  4. Dimov, I. T., et al., A New Iterative Monte Carlo Approach for Inverse Matrix Problem, Journal of Computational and Applied Mathematics, 92 (1998), 1, pp. 15-35
  5. Dimov, I. T., et al., Monte Carlo Algorithms: Performance Analysis for some Computer Architectures, Journal of Computational and Applied Mathematics, 48 (1993), 3, pp. 253-277
  6. Farnoosh, R., et al., Monte Carlo Simulation Via a Numerical Algorithm for Solving a Nonlinear Inverse Problem, Commun Nonlinear Sci Numer Simulat, 15 (2010), 9, pp. 2436-2444
  7. Shidfar, A., et al., A Numerical Method for Solving of a Nonlinear Inverse Diffusion Problem, Computers and Mathematics with Applications, 52 (2006), 6-7, pp. 1021-1030
  8. Shidfar, A., et al., A Numerical Solution Technique for a One-Dimensional Inverse Nonlinear Parabolic Problem, Applied Mathematica and Computation, 184 (2007), 2, pp. 308-315
  9. Hu, B., et al., Crank-Nicolson Finite Difference Scheme for the Rosenau-Burgers Equation, Applied Mathematica and Computation, 204 (2008), 1, pp. 311-316
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Monte Carlo method for solving a parabolic problem

© 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