An Analytical Approach to Solve the Fractional Benney Equation Using the q-Homotopy Analysis Transform Method
Abstract
:1. Introduction
2. Preliminaries
3. Methodology
4. Numerical Problems
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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1 | 0 | 2.128379167 | 2.140766367 | 2.071557441 | 2 |
0.1 | 85.31665749 | 75.96945949 | 54.8749427 | 40.6761086 | |
0.2 | 177.0418155 | 157.3943186 | 113.1421651 | 83.3731548 | |
0.3 | 278.2481880 | 247.2507879 | 177.4677326 | 130.5258330 | |
0.4 | 390.2002534 | 346.6438118 | 248.6191438 | 182.6863557 | |
0.5 | 515.0072901 | 457.3916866 | 327.8236424 | 240.7187498 | |
0.6 | 656.8171393 | 583.0369874 | 417.4220704 | 306.2414199 | |
0.7 | 824.6185442 | 731.2090832 | 522.3800063 | 382.6390723 | |
0.8 | 1038.759922 | 919.0860269 | 653.7294243 | 477.335391 | |
0.9 | 1345.435884 | 1185.467730 | 836.0769337 | 606.689905 | |
1 | 1846.975581 | 1615.918535 | 1123.085975 | 806.000000 |
q-HATM | LADM | |||||
---|---|---|---|---|---|---|
1 | 0 | 15.89865417 | 14.25381518 | 10.52430944 | 8 | 8 |
0.1 | −1.832024984 | −1.543389489 | −0.8803186628 | −0.4295903926 | −0.4295903926 | |
0.2 | −19.14110255 | −16.95979593 | −12.00254110 | −8.646209940 | −8.646209940 | |
0.3 | −34.63295823 | −30.75026556 | −21.94082484 | −15.98192520 | −15.98192520 | |
0.4 | −47.06736293 | −41.81265793 | −29.90352005 | −21.85367303 | −21.85367303 | |
0.5 | −55.44182498 | −49.26000190 | −35.25928442 | −25.79968055 | −25.79968055 | |
0.6 | −59.07713582 | −52.49340697 | −37.58497881 | −27.51235592 | −27.51235592 | |
0.7 | −57.68973832 | −51.26276939 | −36.70405550 | −26.86375081 | −26.86375081 | |
0.8 | −51.42898240 | −45.69773137 | −32.70565981 | −23.91791002 | −23.91791002 | |
0.9 | −40.86344304 | −36.29615175 | −25.93720850 | −18.92581335 | −18.92581335 | |
1 | −26.91555476 | −23.86942018 | −16.96996307 | −12.30256052 | −12.30256052 |
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Shah, R.; Alkhezi, Y.; Alhamad, K. An Analytical Approach to Solve the Fractional Benney Equation Using the q-Homotopy Analysis Transform Method. Symmetry 2023, 15, 669. https://doi.org/10.3390/sym15030669
Shah R, Alkhezi Y, Alhamad K. An Analytical Approach to Solve the Fractional Benney Equation Using the q-Homotopy Analysis Transform Method. Symmetry. 2023; 15(3):669. https://doi.org/10.3390/sym15030669
Chicago/Turabian StyleShah, Rasool, Yousuf Alkhezi, and Khaled Alhamad. 2023. "An Analytical Approach to Solve the Fractional Benney Equation Using the q-Homotopy Analysis Transform Method" Symmetry 15, no. 3: 669. https://doi.org/10.3390/sym15030669
APA StyleShah, R., Alkhezi, Y., & Alhamad, K. (2023). An Analytical Approach to Solve the Fractional Benney Equation Using the q-Homotopy Analysis Transform Method. Symmetry, 15(3), 669. https://doi.org/10.3390/sym15030669