Hyperbolic B-Spline Function-Based Differential Quadrature Method for the Approximation of 3D Wave Equations
Abstract
:1. Introduction
2. The Hyperbolic B-Spline Differential Quadrature Method
3. Stability Analysis
4. Computational Results
Computational Complexity
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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0 | 0 | ||||
0 | 0 | 0 |
Present Method | EFG Method [16] | MLPG Method [16] | Expo-MCBDQM [17] | |
---|---|---|---|---|
0.1 | 9.131 × 10−7 | 1.361376 × 10−1 | 6.389040 × 10−4 | 1.013 × 10−6 |
0.2 | 9.126 × 10−7 | 1.108673 × 10−1 | 1.621007 × 10−3 | 1.666 × 10−6 |
0.3 | 9.751 × 10−7 | 9.031794 × 10−2 | 2.069397 × 10−3 | 1.725 × 10−6 |
0.4 | 9.357 × 10−7 | 7.555177 × 10−2 | 1.851491 × 10−3 | 1.498 × 10−6 |
0.5 | 9.263 × 10−7 | 6.113317 × 10−2 | 1.406413 × 10−3 | 1.196 × 10−6 |
0.6 | 8.105 × 10−7 | 5.076050 × 10−2 | 1.120239 × 10−3 | 9.059 × 10−7 |
0.7 | 6.102 × 10−7 | 4.276296 × 10−2 | 8.762877 × 10−4 | 7.061 × 10−7 |
0.8 | 4.458 × 10−7 | 3.416178 × 10−2 | 5.762842 × 10−4 | 5.566 × 10−7 |
0.9 | 3.614 × 10−7 | 3.072394 × 10−2 | 7.778958 × 10−4 | 4.758 × 10−7 |
1.0 | 3.326 × 10−7 | 2.562088 × 10−2 | 8.638225 × 10−4 | 4.417 × 10−7 |
Present Method | EFG Method [16] | MLPG Method [17] | Expo-MCBDQM [17] | |
---|---|---|---|---|
0.1 | 4.472 × 10−6 | 1.653265 × 100 | 2.777931 × 10−3 | 5.667 × 10−6 |
0.2 | 8.511 × 10−6 | 1.005632 × 100 | 8.477482 × 10−3 | 9.701 × 10−6 |
0.3 | 2.23 × 10−6 | 9.786343 × 10−1 | 1.352534 × 10−2 | 1.231 × 10−5 |
0.4 | 5.02 × 10−6 | 7.456237 × 10−1 | 1.583307 × 10−2 | 1.512 × 10−5 |
0.5 | 1.143 × 10−5 | 6.213675 × 10−1 | 1.550351 × 10−2 | 1.824 × 10−5 |
0.6 | 1.062 × 10−5 | 4.354421 × 10−1 | 1.367202 × 10−2 | 2.222 × 10−5 |
0.7 | 1.231 × 10−5 | 1.345213 × 10−1 | 1.052578 × 10−2 | 2.570 × 10−5 |
0.8 | 1.324 × 10−5 | 9.973233 × 10−2 | 6.216680 × 10−3 | 2.866 × 10−5 |
0.9 | 2.014 × 10−5 | 7.132423 × 10−2 | 5.280951 × 10−3 | 3.117 × 10−5 |
1.0 | 2.1025 × 10−5 | 6.124572 × 10−2 | 2.276681 × 10−3 | 3.329 × 10−5 |
Present Method | EFG Method [16] | MLPG Method [16] | Expo-MCBDQM [17] | |
---|---|---|---|---|
0.1 | 1.673 × 10−7 | 1.435666 × 10−3 | 8.903029 × 10−5 | 2.887 × 10−7 |
0.2 | 2.481 × 10−7 | 3.867576 × 10−3 | 9.910264 × 10−5 | 1.257 × 10−6 |
0.3 | 1.522 × 10−6 | 5.033494 × 10−3 | 1.590358 × 10−4 | 2.944 × 10−6 |
0.4 | 4.137 × 10−6 | 7.655177 × 10−3 | 3.776687 × 10−4 | 5.348 × 10−6 |
0.5 | 7.465 × 10−6 | 9.119769 × 10−3 | 4.781290 × 10−4 | 8.787 × 10−6 |
0.6 | 3.304 × 10−6 | 1.034540 × 10−2 | 6.416380 × 10−4 | 1.361 × 10−5 |
0.7 | 1.007 × 10−5 | 3.279875 × 10−2 | 8.809498 × 10−4 | 2.029 × 10−5 |
0.8 | 1.716 × 10−5 | 5.233178 × 10−2 | 9.279331 × 10−4 | 2.918 × 10−5 |
0.9 | 3.014 × 10−5 | 6.072234 × 10−2 | 1.059260 × 10−4 | 4.049 × 10−5 |
1.0 | 4.221 × 10−5 | 7.545088 × 10−2 | 1.529316 × 10−3 | 5.432 × 10−5 |
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Tamsir, M.; Meetei, M.Z.; Msmali, A.H. Hyperbolic B-Spline Function-Based Differential Quadrature Method for the Approximation of 3D Wave Equations. Axioms 2022, 11, 597. https://doi.org/10.3390/axioms11110597
Tamsir M, Meetei MZ, Msmali AH. Hyperbolic B-Spline Function-Based Differential Quadrature Method for the Approximation of 3D Wave Equations. Axioms. 2022; 11(11):597. https://doi.org/10.3390/axioms11110597
Chicago/Turabian StyleTamsir, Mohammad, Mutum Zico Meetei, and Ahmed H. Msmali. 2022. "Hyperbolic B-Spline Function-Based Differential Quadrature Method for the Approximation of 3D Wave Equations" Axioms 11, no. 11: 597. https://doi.org/10.3390/axioms11110597
APA StyleTamsir, M., Meetei, M. Z., & Msmali, A. H. (2022). Hyperbolic B-Spline Function-Based Differential Quadrature Method for the Approximation of 3D Wave Equations. Axioms, 11(11), 597. https://doi.org/10.3390/axioms11110597