New iterative technique for computing Fourier transforms.
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, Ai...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Anbar
2023-12-01
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| Series: | مجلة جامعة الانبار للعلوم الصرفة |
| Subjects: | |
| Online Access: | https://juaps.uoanbar.edu.iq/article_181586_27ede256d55b878de0b9ab80cf2bcadd.pdf |
| _version_ | 1797373131281661952 |
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| author | Ahmad Issa Murat Düz |
| author_facet | Ahmad Issa Murat Düz |
| author_sort | Ahmad Issa |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T18:46:00Z |
| format | Article |
| id | doaj.art-570310fbb47d479d8efc1f8df1e2c7b8 |
| institution | Directory Open Access Journal |
| issn | 1991-8941 2706-6703 |
| language | English |
| last_indexed | 2024-03-08T18:46:00Z |
| publishDate | 2023-12-01 |
| publisher | University of Anbar |
| record_format | Article |
| series | مجلة جامعة الانبار للعلوم الصرفة |
| spelling | doaj.art-570310fbb47d479d8efc1f8df1e2c7b82023-12-28T22:02:45ZengUniversity of Anbarمجلة جامعة الانبار للعلوم الصرفة1991-89412706-67032023-12-0117235535910.37652/juaps.2023.181586181586New iterative technique for computing Fourier transforms.Ahmad Issa0Murat Düz1Department of Mathematics, Faculty of Science, Karabuk University, Karabuk, Turkey ;Department of Mathematics, Faculty of Science, Karabuk University, Karabuk, Turkey ;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.https://juaps.uoanbar.edu.iq/article_181586_27ede256d55b878de0b9ab80cf2bcadd.pdfordinary differential equationsadomian decomposition methodfourier transform |
| spellingShingle | Ahmad Issa Murat Düz New iterative technique for computing Fourier transforms. مجلة جامعة الانبار للعلوم الصرفة ordinary differential equations adomian decomposition method fourier transform |
| title | New iterative technique for computing Fourier transforms. |
| title_full | New iterative technique for computing Fourier transforms. |
| title_fullStr | New iterative technique for computing Fourier transforms. |
| title_full_unstemmed | New iterative technique for computing Fourier transforms. |
| title_short | New iterative technique for computing Fourier transforms. |
| title_sort | new iterative technique for computing fourier transforms |
| topic | ordinary differential equations adomian decomposition method fourier transform |
| url | https://juaps.uoanbar.edu.iq/article_181586_27ede256d55b878de0b9ab80cf2bcadd.pdf |
| work_keys_str_mv | AT ahmadissa newiterativetechniqueforcomputingfouriertransforms AT muratduz newiterativetechniqueforcomputingfouriertransforms |