THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Feng Gao

,

Xiao-Jun Yang

LOCAL FRACTIONAL EULER'S METHOD FOR THE STEADY HEAT-CONDUCTION PROBLEM

ABSTRACT
In this paper, the local fractional Euler's method is proposed to consider the steady heat-conduction problem for the first time. The numerical solution for the local fractional heat-relaxation equation is presented. The comparison between numerical and exact solutions is discussed.
KEYWORDS
heat-conduction problem, heat-relaxation equation, numerical solution, local fractional Euler’s method, local fractional derivative
PAPER SUBMITTED: 2015-12-21
PAPER REVISED: 2016-01-05
PAPER ACCEPTED: 2016-01-28
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3735G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S735 - S738]
REFERENCES
  1. Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Academic Press, New York, USA, 2015
  2. Zhang, Y., et al., An Efficient Analytical Method for Solving Local Fractional Nonlinear PDEs Arising in Mathematical Physics, Applied Mathematical Modelling, 40 (2016), 3, pp. 1793-1799
  3. Zhao, D., et al., On the Fractal Heat-Transfer Problems with Local Fractional Calculus, Thermal Science, 19 (2015), 5, pp. 1867-1871
  4. Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47 (2015), Sep., pp. 54-60
  5. Jafari, H., et al., A Decomposition Method for Solving Diffusion Equations via Local Fractional Time Derivative, Thermal Science, 19 (2015), Suppl. 1, pp. S123-S129
  6. Yang, X. J., et al., A New Numerical Technique for Solving the Local Fractional Diffusion Equation: Two-Dimensional Extended Differential Transform Approach, Applied Mathematics and Computation, 274 (2016), Feb., pp. 143-151
  7. Zhang, Y., et al., Local Fractional Variational Iteration Algorithm II for Non-Homogeneous Model Associated with the Non-Differentiable Heat Flow, Advances in Mechanical Engineering, 7 (2015), 10, pp. 1-7
  8. Sarikaya, M. Z., et al., On Generalized some Integral Inequalities for Local Fractional Integrals, Applied Mathematics and Computation, 276 (2016), Mar., pp. 316-323
  9. Yang, X. J., Advanced Local Fractional Calculus and its Applications, World Science, New York, USA, 2012
  10. Wang, Y., et al., Solving Fractal Steady Heat-Transfer Problems with the Local Fractional Sumudu Transform, Thermal Science, 19 (2015), Suppl. 2, pp. S637-S641
  11. Yang, X. J., et al., An Asymptotic Perturbation Solution for a Linear Oscillator of Free Damped Vibrations in Fractal Medium Described by Local Fractional Derivatives, Communications in Nonlinear Science and Numerical Simulation, 29 (2015), 1, pp. 499-504
  12. Erden, S., et al., Generalized Pompeiu Type Inequalities for Local Fractional Integrals and its Applications, Applied Mathematics and Computation, 274 (2016), Feb., pp. 282-291
  13. Robinson, J. C., An Introduction to Ordinary Differential Equations, Cambridge University Press, Cambridge, UK, 2004
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Local fractional Euler's method for the steady heat-conduction 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