Document Type : Research Paper
Authors
Department of Mathematics, Faculty of Science, Karabuk University, Karabuk, Turkey ;
Abstract
The Fourier transformations have stimulated many amounts of articles in recent years. they arise in the fields of engineering, control systems, and technology like analyzing signals in electronic circuits, radio circuits, cell phones, image processing, and in solutions to heat transfer equations, Airy equations, Telegraph equations, Duffing equations, Wave equations, Fisher equations, Laplace equation, etc. In this paper, a new iterative method called Adomian Decomposition Method (ADM) is implemented to obtain the Fourier transform of functions by solving a linear ordinary differential equation of first order. This method focuses on finding Fourier transforms by knowing the series resulting from Adomian polynomials. Five famous examples are presented to test the effectiveness and validity of this technique. The results indicate that the accuracy of this method is fully in agreement with the classical method. Furthermore, when applying the Adomian decomposition method, we noticed that it provides accurate results and does not require a lot of time and effort to obtain Fourier transforms of the functions because it does not require a large number of iterations.
Keywords
Main Subjects
- Düz, M., Issa, A., & Avezov, S. (2022). A new computational technique for Fourier transforms by using the Differential transformation method, Bulletin of International Mathematical Virtual Institute, 12(2), 287-295.
- Issa, A., & Düz, M. (2022). Different computational approach for Fourier transforms by using variational iteration method, Journal of New Results in Science, 11(3), 190-198.
- Chen, W., & Lu, Z. (2004). An algorithm for Adomian decomposition method, Applied Mathematics and Computation, 159(1), 221-235.
- Abbasbandy, S. (2006). Application of He’s homotopy perturbation method for Laplace transform, Chaos, Solitons & Fractals, 30(5), 1206-1212.
- Babolian, E., Biazar, J., & Vahidi, A. (2004). A new computational method for Laplace transforms by decomposition method, Applied Mathematics and Computation, 150(3), 841-846.
- Issa, A., & Al Horani, M. (2023). Sinc collocation method for solving linear systems of Fredholm Volterra integro–differential equations of high order with variable coefficients, Results in Nonlinear Analysis, 6(1), 49-58.
- Osgood, B. (2009). The Fourier transform and its applications, Lecture notes for EE, 261, 20.
- Wheeler, N. (1997). Simplified production of Dirac delta function identities, Reed College.
- Adomian, G. (1988). Nonlinear stochastic systems theory and applications to physics, Springer Science & Business Media, 46.
- Adomian, G. (2013). Solving frontier problems of physics: the decomposition method, Springer Science & Business Media, 60.
- Haldar, K., & Datta, B.K. (1996). Integrations by asymptotic decomposition, Math. Lett, 9(2) 81–83.
- Cherruault, Y. (1989). Convergence of Adomian's method, Kybernets, 18(2), 31–39.
- Cherruault, Y. (1992). Some new results for convergence of Adomians method applied to integral equations, Comput. Modeling, 16(2), 85–93.
- Bracewell, R.N. (1989). The fourier transform, Scientific American, 260(6), 86-95.
- Ernst, R.R., & Anderson, W.A. (1966). Application of Fourier transform spectroscopy to magnetic resonance, Review of Scientific Instruments, 37(1), 93-102.
- Avezov, S., Düz, M., & Issa, A. (2023). Solutions to Differential-Differential Difference Equations with Variable Coefficients by Using Fourier Transform Method, Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, 18(3), 259-267.
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