THERMAL SCIENCE
International Scientific Journal
APPLICATIONS OF THE FOURIER-LIKE INTEGRAL TRANSFORM IN THE WAVE AND HEAT-TRANSFER PROBLEMS
ABSTRACT
In this article, some new properties of a novel integral transform termed the Fourier-Yang are explored. The Fourier-Yang integral transforms of several basic functions are given firstly. With the aid of the new integral transform, a 1-D wave equation and 2-D heat transfer equation are solved. The results show that the Fourier-Yang integral transform is efficient in solving PDE.
KEYWORDS
PAPER SUBMITTED: 2018-05-20
PAPER REVISED: 2018-06-28
PAPER ACCEPTED: 2018-08-11
PUBLISHED ONLINE: 2019-03-31
THERMAL SCIENCE YEAR
2019, VOLUME
23, ISSUE
Supplement 3, PAGES [S703 - S709]
- Debnath, L., Bhatta, D., Integral Transforms and Their Applications, CRC Press, Boca Raton, Fla., USA, 2014
- Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), pp. 193-197
- Jin, Z. H., Paulino, G. H., Transient Thermal Stress Analysis of an Edge Crack in a Functionally Graded Material, International Journal of Fracture, 107 (2001), 1, pp. 73-98
- Kulish, V. V., Lage, J. L., Application of Fractional Calculus to Fluid Mechanics, Journal of Fluids Engineering, 124 (2002), 3, pp. 803-806
- Zhao, C., Yang, C., Exact Solutions for Electro-Osmotic Flow of Viscoelastic Fluids in Rectangular Micro-Channels, Applied Mathematics & Computation, 211 (2009), 2, pp. 502-509
- Greengard, L., Lee, J. Y., Accelerating the Nonuniform Fast Fourier Transform, Siam Review, 46 (2004), 3, pp. 443-454
- Fan, Z., et al., Weak Form Nonuniform Fast Fourier Transform Method for Solving Volume Integral Equations, Progress in Electromagnetics Research, 89 (2009), 4, pp. 275-289
- Yokogawa, D., et al., An Integral Equation Theory for 3D Solvation Structure: A New Procedure Free from 3D Fourier Transform, Chemical Physics Letters, 432 (2006), 4, pp. 595-599
- Eltayeb, H., et al., A New Integral Transform and Associated Distributions, Integral Transforms & Special Functions, 21 (2010), 5, pp. 367-379
- Kumar, D., et al., An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform, Abstract and Applied Analysis, (2013), pp. 1-16
- Boyadjiev, L., Luchko, Y., Mellin Integral Transform Approach to Analyze the Multidimensional Diffusion-Wave Equations, Chaos Solitons & Fractals, 102 (2017), pp. 127-134
- Elzaki, T. M., The new Integral Transform "Elzaki Transform", Global Journal of Pure & Applied Mathematics, 7 (2011), 1, pp. 57-64
- Tarig, E., et al., On the New Integral Transform "ELzaki Transform" Fundamental Properties Investigations and Applications, Global Journal of Mathematical Sciences, 2012
- Celeghini, E., Del Olmo, M.A., Quantum Physics and Signal Processing in Rigged Hilbert Spaces by Means of Special Functions, Lie Algebras and Fourier and Fourier-Like Transforms, Journal of Physics: Conference Series, 597 (2015), pp. 012022
- Liang, X., et al., Applications of a Novel Integral Transform to Partial Differential Equations, Journal of Nonlinear Science & Applications, 10 (2017), 2, pp. 528-534
- Friba, L., Vibration of Solids and Structures under Moving Loads, Springer Science & Business Media ,1(1972), pp. 39-99
- Yang, X. J., New Integral Transforms for Solving a Steady Heat Transfer Problem, Thermal Science, 21 (2017), Suppl.1, pp. S79-S87
- Beerends, R. J., et al., Fourier and Laplace Transforms, Cambridge University Press, Cambridge, UK, 2003
- Dyke, P. P. G., An Introduction to Laplace Transforms and Fourier Series// an Introduction to Laplace transforms and Fourier series, Springer, 2001
- Usman, M., et al., Differential Transform Method for Unsteady Nanofluid Flow and Heat Transfer, Alexandria Engineering Journal, 57(2018), 3, PP.1867-1875
