Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation Technique
A new technique to study the telegraph equation, mostly familiar as damped wave equation is introduced in this study. This phenomenon is mostly rising in electromagnetic influences and production of electric signals. The proposed technique called as He-Fractional Laplace technique with help of Hom...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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University of Baghdad
2023-07-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3239 |
| _version_ | 1797776211702710272 |
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| author | Ali Moazzzam Ayza Anjum Nimra Saleem Emad A. Kuffi |
| author_facet | Ali Moazzzam Ayza Anjum Nimra Saleem Emad A. Kuffi |
| author_sort | Ali Moazzzam |
| collection | DOAJ |
| description |
A new technique to study the telegraph equation, mostly familiar as damped wave equation is introduced in this study. This phenomenon is mostly rising in electromagnetic influences and production of electric signals. The proposed technique called as He-Fractional Laplace technique with help of Homotopy perturbation is utilized to found the exact and nearly approximated results of differential model and numerical example of telegraph equation or damped wave equation in this article. The most unique term of this technique is that, there is no worry to find the next iteration by integration in recurrence relation. As fractional Laplace integral transformation has some limitations in non-linear terms, to get the result of nonlinear term in this differential mode, He polynomials via homotopy techniques of iteration is proposed to find the result of the computation assignment. The obtained result by this proposed technique directed that this technique is quite ease to apply and convergent rapidly to exact solutions. Numerous examples are described to determine the stability and accuracy of the proposed technique with the graphical explanation.
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| first_indexed | 2024-03-12T22:46:42Z |
| format | Article |
| id | doaj.art-fc96f2ebc857491492e39f965d6a6fb7 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-03-12T22:46:42Z |
| publishDate | 2023-07-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-fc96f2ebc857491492e39f965d6a6fb72023-07-21T05:07:01ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072023-07-0136310.30526/36.3.3239Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation TechniqueAli Moazzzam0Ayza AnjumNimra Saleem1Emad A. Kuffi2University of Agriculture Faisalabad, PakistanUniversity of Agriculture Faisalabad, PakistanAl-Qadisiyah University, College of Engineering, Iraq. A new technique to study the telegraph equation, mostly familiar as damped wave equation is introduced in this study. This phenomenon is mostly rising in electromagnetic influences and production of electric signals. The proposed technique called as He-Fractional Laplace technique with help of Homotopy perturbation is utilized to found the exact and nearly approximated results of differential model and numerical example of telegraph equation or damped wave equation in this article. The most unique term of this technique is that, there is no worry to find the next iteration by integration in recurrence relation. As fractional Laplace integral transformation has some limitations in non-linear terms, to get the result of nonlinear term in this differential mode, He polynomials via homotopy techniques of iteration is proposed to find the result of the computation assignment. The obtained result by this proposed technique directed that this technique is quite ease to apply and convergent rapidly to exact solutions. Numerous examples are described to determine the stability and accuracy of the proposed technique with the graphical explanation. https://jih.uobaghdad.edu.iq/index.php/j/article/view/3239Fractional Laplace method, He’s Polynomials, Homotopy Perturbation, Approximated solutions, Telegraph Equation. |
| spellingShingle | Ali Moazzzam Ayza Anjum Nimra Saleem Emad A. Kuffi Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation Technique Ibn Al-Haitham Journal for Pure and Applied Sciences Fractional Laplace method, He’s Polynomials, Homotopy Perturbation, Approximated solutions, Telegraph Equation. |
| title | Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation Technique |
| title_full | Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation Technique |
| title_fullStr | Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation Technique |
| title_full_unstemmed | Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation Technique |
| title_short | Study of Telegraph Equation via He-Fractional Laplace Homotopy Perturbation Technique |
| title_sort | study of telegraph equation via he fractional laplace homotopy perturbation technique |
| topic | Fractional Laplace method, He’s Polynomials, Homotopy Perturbation, Approximated solutions, Telegraph Equation. |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3239 |
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