THERMAL SCIENCE

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Chun-Hui He

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Ji-Huan He

DOUBLE TRIALS METHOD FOR NONLINEAR PROBLEMS ARISING IN HEAT TRANSFER

ABSTRACT
According to an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD, two trial roots are assumed to solve algebraic equations. The solution procedure can be extended to solve nonlinear differential equations by constructing an approximate solution with an unknown parameter, and the unknown parameter can be easily determined using the Ying Buzu Shu. An example in heat transfer is given to elucidate the solution procedure.
KEYWORDS
ancient Chinese mathematics, approximate solution
PAPER SUBMITTED: 2011-02-06
PAPER REVISED: 2011-02-07
PAPER ACCEPTED: 2011-02-07
DOI REFERENCE: https://doi.org/10.2298/TSCI11S1153H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2011, VOLUME 15, ISSUE Supplement 1, PAGES [S153 - S155]
REFERENCES
  1. He, J.-H., Ancient Chinese Algorithm: the Ying Buzu Shu (Method of Surplus and Deficiency) vs. Newton Iteration Method, Applied Math. Mech., 23 (2002), 12, pp. 1255-1260
  2. He, J.-H., Some Asymptotic Methods for Strongly Nonlinear Equations, Int. J. Mod. Phys. B., 20 (2006), 10, pp. 1141-1199
  3. He, J.-H., An Elementary Introduction to Recently Developed Asymptotic Methods and Nano-Mechanics in Textile Engineering, Int. J. Mod. Phys. B. 22 (2008), 21, pp. 3487-3578
  4. Ganji, D. D., Sadighi, A., Application of Homotopy-Perturbation and Variational Iteration Methods to Nonlinear Heat Transfer and Porous Media Equations, J. Comput. Appl. Math., 207 (2007), 1, pp. 24-34
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Double trials method for nonlinear problems arising in heat transfer

© 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