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ANALYTICAL SOLUTIONS OF LINEAR DIFFUSION AND WAVE EQUATIONS IN SEMI-INFINITE DOMAINS BY USING A NEW INTEGRAL TRANSFORM

ABSTRACT
Recently, a new integral transform similar to Sumudu transform has been proposed by Yang [1]. Some of the properties of the integral transform are expanded in the present article. Meanwhile, new applications to the linear wave and diffusion equations in semi-infinite domains are discussed in detail. The proposed method provides an alternative approach to solve the partial differential equations in mathematical physics.
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PAPER SUBMITTED: 2017-03-10
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-05-11
PUBLISHED ONLINE: 2017-12-02
DOI REFERENCE: https://doi.org/10.2298/TSCI17S1071G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S71 - S78]
REFERENCES
  1. Yang, X. J., A New Integral Transform Method for Solving Steady Heat Transform Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S639-S642
  2. Debnath, L., Bhatta, D., Integral Transforms and Their Applications, CRC Press, Boca Raton, Fla., USA, 2014
  3. Watugala, G. K., Sumudu Transform: A New Integral Transform to Solve Differential Equation and Control Engineering Problems, Integrated Education, 24 (1993), 1, pp. 35-43
  4. Eltayed, H., Kilicman, A., A Note on Solutions of Wave, Laplace's and Heat Equations with Convolution Terms by Using a Double Laplace Transform, Applied Mathematics Letters, 21 (2008), 12, pp. 1324-1329
  5. Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197
  6. Liang, X, et al., Applications of a Novel Integral Transform to Partial Differential Equations, Journal of Nonlinear Science and Applications, 10 (2017), 2, pp. 528-534
  7. Beerends, R. J., et al., Fourier and Laplace Transform, Cambridge University Press, Oxford, UK, 2003
  8. Yang, X. J., A New Integral Transform with an Application in Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S677-S681
  9. Yang, X. J., Gao, F. A New Technology for Solving Diffusion and Heat Equations, Thermal Science, 21 (2017), 1A, pp. 133-140
  10. Asiri, S., et al., Inverse Source Problem for a One-Dimensional Wave Equation Using Observers, Proceedings, 11th International Conference on Mathematical and Numerical Aspects of Waves, Propagation, 11 (2013), pp. 149-150

© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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