Construction of an Approximate Analytical Solution for Multi-Dimensional Fractional Zakharov–Kuznetsov Equation via Aboodh Adomian Decomposition Method
Abstract
:1. Introduction
2. Prelude
3. Configuration for Aboodh Adomian Decomposition Method
4. Qualitative Aspects of Aboodh-Adomian Decomposition Method
5. Numerical Illustrations
6. Other Aspects of ZKEs
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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t | AADM Solution | Exact Solution | PIA [37] Error | RPSM [37] Error | AADM Error | ||
---|---|---|---|---|---|---|---|
0.1 | 0.1 | 0.2 | 5.3966 × | 5.39388 × | 3.85217 × | 3.85217 × | 2.71884 × |
0.1 | 0.1 | 0.3 | 5.39248 × | 5.38841 × | 5.75911 × | 5.75912 × | 4.07394 × |
0.1 | 0.1 | 0.4 | 5.38837 × | 5.38294 × | 7.65359 × | 7.65352 × | 5.42615 × |
0.6 | 0.6 | 0.2 | 3.02967 × | 3.03651 × | 4.66337 × | 4.66389 × | 6.83433 × |
0.6 | 0.6 | 0.3 | 3.02553 × | 3.03578 × | 6.86056 × | 6.86314 × | 1.02517 × |
0.6 | 0.6 | 0.4 | 3.02138 × | 3.03505 × | 8.98263 × | 8.99046 × | 1.36692 × |
0.9 | 0.9 | 0.2 | 1.14455 × | 1.15370 × | 5.12131 × | 5.14241 × | 9.14704 × |
0.9 | 0. 9 | 0.3 | 1.13973 × | 1.15345 × | 7.38186 × | 7.48450 × | 1.37206 × |
0.9 | 0.9 | 0.4 | 1.13492 × | 1.15321 × | 9.57942 × | 9.89139 × | 1.82943 × |
t | AADM Solution | PIA [37] | RPSM [37] | AADM Solution | PIA [37] | RPSM [37] | |
---|---|---|---|---|---|---|---|
0.1 | 0.2 | 5.39424 × | 5.31854 × | 5.31244 × | 5.3953 × | 5.32747 × | 5.32479 × |
0.1 | 0.3 | 5.39094 × | 5.28631 × | 5.28410 × | 5.39191 × | 5.29757 × | 5.29675 × |
0.1 | 0.4 | 5.38798 × | 5.25777 × | 5.25897 × | 5.38881 × | 5.27039 × | 5.27119 × |
0.6 | 0.2 | 3.02730 × | 2.95493 × | 2.95185 × | 3.02837 × | 2.96356 × | 2.96251 × |
0.6 | 0.3 | 3.02397 × | 2.92662 × | 2.92709 × | 3.02496 × | 2.93717 × | 2.93780 × |
0.6 | 0.4 | 3.02099 × | 2.90307 × | 2.90522 × | 3.02182 × | 2.91448 × | 2.91561 × |
0.9 | 0.2 | 1.14179 × | 1.06822 × | 1.05522 × | 1.14303 × | 1.07716 × | 2.91561 × |
0.9 | 0.3 | 1.13792 × | 1.04487 × | 1.01199 × | 1.13907 × | 1.05488 × | 1.03695 × |
0.9 | 0.4 | 1.13447 × | 9.02777 × | 9.60606 × | 1.13543 × | 1.03736 × | 9.96743 × |
t | AADM Solution | Exact Solution | VIM [41] Error | AADM Error | ||
---|---|---|---|---|---|---|
0.1 | 0.1 | 0.2 | 5.00092 × | 4.99592 × | 5.00091 × | 4.99519 × |
0.1 | 0.1 | 0.3 | 5.00091 × | 4.99342 × | 5.00091 × | 7.49278 × |
0.1 | 0.1 | 0.4 | 5.00091 × | 4.99092 × | 5.00091 × | 9.99037 × |
0.6 | 0.6 | 0.2 | 3.02004 × | 3.01953 × | 3.02003 × | 5.08987 × |
0.6 | 0.6 | 0.3 | 3.02004 × | 3.01927 × | 3.02003 × | 7.63479 × |
0.6 | 0.6 | 0.4 | 3.02004 × | 3.01902 × | 3.02003 × | 1.01797 × |
0.9 | 0.9 | 0.2 | 4.5678 × | 4.56728 × | 4.56780 × | 5.21227 × |
0.9 | 0. 9 | 0.3 | 4.5678 × | 4.56702 × | 4.56780 × | 7.81839 × |
0.9 | 0.9 | 0.4 | 4.5678 × | 4.56676 × | 4.56780 × | 1.04245 × |
t | AADM for | VIM [41] for | AADM for | VIM [41] for | |
---|---|---|---|---|---|
0.1 | 0.2 | 5.00091 × | 5.00091 × | 5.00091 × | 5.00091 × |
0.1 | 0.3 | 5.00091 × | 5.00090 × | 5.00091 × | 5.00090 × |
0.1 | 0.4 | 5.0009 × | 5.00090 × | 5.00091 × | 5.00090 × |
0.6 | 0.2 | 3.02004 × | 3.02003 × | 3.02004 × | 3.02003 × |
0.6 | 0.3 | 3.02004 × | 3.02003 × | 3.02004 × | 3.02003 × |
0.6 | 0.4 | 3.02004 × | 3.02003 × | 3.02004 × | 3.02003 × |
0.9 | 0.2 | 4.5678 × | 4.56780 × | 4.5678 × | 4.5678 × |
0. 9 | 0.3 | 4.5678 × | 4.56780 × | 4.5678 × | 4.5678 × |
0.9 | 0.4 | 4.5678 × | 4.56780 × | 4.5678 × | 4.5678 × |
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Rashid, S.; Kubra, K.T.; Guirao, J.L.G. Construction of an Approximate Analytical Solution for Multi-Dimensional Fractional Zakharov–Kuznetsov Equation via Aboodh Adomian Decomposition Method. Symmetry 2021, 13, 1542. https://doi.org/10.3390/sym13081542
Rashid S, Kubra KT, Guirao JLG. Construction of an Approximate Analytical Solution for Multi-Dimensional Fractional Zakharov–Kuznetsov Equation via Aboodh Adomian Decomposition Method. Symmetry. 2021; 13(8):1542. https://doi.org/10.3390/sym13081542
Chicago/Turabian StyleRashid, Saima, Khadija Tul Kubra, and Juan Luis García Guirao. 2021. "Construction of an Approximate Analytical Solution for Multi-Dimensional Fractional Zakharov–Kuznetsov Equation via Aboodh Adomian Decomposition Method" Symmetry 13, no. 8: 1542. https://doi.org/10.3390/sym13081542
APA StyleRashid, S., Kubra, K. T., & Guirao, J. L. G. (2021). Construction of an Approximate Analytical Solution for Multi-Dimensional Fractional Zakharov–Kuznetsov Equation via Aboodh Adomian Decomposition Method. Symmetry, 13(8), 1542. https://doi.org/10.3390/sym13081542