Fractional Telegraph Equation and Its Solution by Natural Transform Decomposition Method
Abstract
:1. Introduction
2. Preliminaries
3. Natural Transform Adomian Decomposition Method Linear and Nonlinear Telegraph Equations (NTADM)
4. Convergence Analysis
5. Numerical Examples
6. Numerical Result
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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t | Exact Solution | Approximate Sol | |
---|---|---|---|
0.0 | 1.648721270700128 | 1.648721270700128 | 0.0 |
0.5 | 1.0 | 1.000000000040401 | 4.040101586 |
1.0 | 0.606530659712633 | 0.606530742852590 | 8.313995659 |
1.5 | 0.367879441171442 | 0.367886690723836 | 7.249552393 |
2.0 | 0.223130160148429 | 0.223303762933655 | 1.569783692 |
t | |||
---|---|---|---|
0.0 | 1.648721270700128 | 1.648721270700128 | 1.648721270700128 |
0.5 | 1.002243362235993 | 1.004498274095028 | 1.006764389796932 |
1.0 | 0.609569757949665 | 0.612585971492061 | 0.615579284214978 |
1.5 | 0.369222108754806 | 0.371788163947318 | 0.370522335669580 |
2.0 | 0.221291547575669 | 0.219269844467107 | 0.217240584657229 |
t | Exact Solution | |||
---|---|---|---|---|
0.0 | 0.5 | 0.5 | 0.5 | 1.5 |
5.0 | 0.824360635350064 | 0.830817752645242 | 0.837755999175080 | 0.845202109327201 |
1.0 | 1.359140914229523 | 1.378259288907402 | 1.398076433466764 | 1.418592017094073 |
1.5 | 2.240844535169032 | 2.276244404149126 | 2.312171661003479 | 2.348587393416824 |
2.0 | 3.694528049465325 | 3.748855797997422 | 3.803171995755493 | 3.857406067787722 |
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Eltayeb, H.; Abdalla, Y.T.; Bachar, I.; Khabir, M.H. Fractional Telegraph Equation and Its Solution by Natural Transform Decomposition Method. Symmetry 2019, 11, 334. https://doi.org/10.3390/sym11030334
Eltayeb H, Abdalla YT, Bachar I, Khabir MH. Fractional Telegraph Equation and Its Solution by Natural Transform Decomposition Method. Symmetry. 2019; 11(3):334. https://doi.org/10.3390/sym11030334
Chicago/Turabian StyleEltayeb, Hassan, Yahya T. Abdalla, Imed Bachar, and Mohamed H. Khabir. 2019. "Fractional Telegraph Equation and Its Solution by Natural Transform Decomposition Method" Symmetry 11, no. 3: 334. https://doi.org/10.3390/sym11030334
APA StyleEltayeb, H., Abdalla, Y. T., Bachar, I., & Khabir, M. H. (2019). Fractional Telegraph Equation and Its Solution by Natural Transform Decomposition Method. Symmetry, 11(3), 334. https://doi.org/10.3390/sym11030334