Numerical Solutions of Coupled Burgers’ Equations
Abstract
:1. Introduction
2. Modified Variational Iteration Algorithm-II
3. Numerical Assessments
3.1. Test Problem 1
3.2. Test Problem 2
3.3. Test Problem 3
4. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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CBCS [5] | LBM [6] | CBSLM [10] | MVIA-II | MVIA-I | CBCS [5] | LBM [6] | CBSLM [10] | MVIA-II | MVIA-I | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|
0.5 | 0.1 | 0.3 | 6.7307 | 6.7736 | 5.7744 | 7.0326 | 2.2440 | 6.5947 | 6.6014 | 5.6194 | 6.7509 | 2.1840 |
1.0 | 0.1 | 0.3 | 1.3173 | 1.3317 | 0.2346 | 1.4073 | 4.4886 | 1.3020 | 1.3045 | 1.2083 | 1.3500 | 4.3681 |
5.0 | 0.1 | 0.3 | 5.9329 | 6.1433 | 6.0584 | 7.0707 | 2.2464 | 6.1046 | 6.1515 | 6.0644 | 6.7445 | 2.1844 |
10 | 0.1 | 0.3 | 1.0760 | 1.1439 | 1.1365 | 1.4221 | 4.4981 | 1.1541 | 1.1713 | 1.1633 | 1.3468 | 4.3694 |
CBCS [5] | LBM [6] | CBSLM [10] | MVIA-II | MVIA-I | CBCS [5] | LBM [6] | CBSLM [10] | MVIA-II | MVIA-I | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.5 | 0.1 | 0.3 | 5.0960 | 5.0505 | 4.3123 | 5.1860 | 2.5955 | 9.1286 | 5.6806 | 4.8567 | 6.2517 | 2.5169 | |
1.0 | 0.1 | 0.3 | 9.9228 | 9.8477 | 9.1399 | 1.0389 | 5.1920 | 1.8244 | 1.0942 | 1.0169 | 1.2509 | 5.0343 | |
5.0 | 0.1 | 0.3 | 4.3800 | 4.3984 | 4.3400 | 5.2635 | 2.5996 | 9.0708 | 4.6640 | 4.6046 | 6.2794 | 2.5190 | |
10 | 0.1 | 0.3 | 7.8592 | 8.0429 | 7.9933 | 7.8956 | 5.2084 | 1.0815 | 8.2714 | 8.2233 | 7.9438 | 5.0426 |
[9] | [3] | [5] | [1] | [2] | MVIA-II | MVIA-I | ||||
---|---|---|---|---|---|---|---|---|---|---|
0.5 | 0.1 | 0.3 | 4:251 | 4:38 | 4:167 | 9:619 | 4:084 | 2.2743 | 1.1511 | |
1.0 | 0.1 | 0.3 | 8:150 | 8:66 | 8:258 | 1:153 | 8:157 | 4.5485 | 2.3024 | |
0.5 | 0.1 | 0.3 | 4:051 | 4:99 | 1:480 | 3:332 | 3:713 | 2.1639 | 6.9734 | |
1.0 | 0.1 | 0.3 | 7:158 | 9:92 | 4:770 | 1:162 | 7:358 | 4.3275 | 1.3949 |
FDM [6] | LBM [6] | MVIA-II | FDM [6] | LBM [6] | MVIA-II | |
---|---|---|---|---|---|---|
1.0 | 1.5724 | 1.4829 | 7.8577 | 6.2856 | 5.7788 | 6.1316 |
2.0 | 2.9383 | 2.7955 | 2.6625 | 1.1138 | 1.0754 | 1.5700 |
3.0 | 4.1676 | 3.9298 | 8.7801 | 1.5879 | 1.4861 | 5.1132 |
4.0 | 5.2504 | 4.9434 | 2.9783 | 1.9868 | 1.8800 | 1.6959 |
5.0 | 6.1878 | 5.8615 | 3.4271 | 2.3468 | 2.2034 | 1.8436 |
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Ahmad, H.; Khan, T.A.; Cesarano, C. Numerical Solutions of Coupled Burgers’ Equations. Axioms 2019, 8, 119. https://doi.org/10.3390/axioms8040119
Ahmad H, Khan TA, Cesarano C. Numerical Solutions of Coupled Burgers’ Equations. Axioms. 2019; 8(4):119. https://doi.org/10.3390/axioms8040119
Chicago/Turabian StyleAhmad, Hijaz, Tufail A. Khan, and Clemente Cesarano. 2019. "Numerical Solutions of Coupled Burgers’ Equations" Axioms 8, no. 4: 119. https://doi.org/10.3390/axioms8040119