The Finite Difference Method and Analysis for Simulating the Unsteady Generalized Maxwell Fluid with a Multi-Term Time Fractional Derivative
Abstract
:1. Introduction
2. Preliminary Knowledge of the Finite-Difference Method
3. Stability Analysis of the Finite Difference Scheme
4. Convergence Analysis of the Finite Difference Scheme
5. Numerical Simulation and Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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, | Order | Order | ||
1/40 | 2.8621 × | 4.0476 × | ||
1/80 | 1.4087 × | 1.023 | 1.9922 × | 1.023 |
1/160 | 6.9717 × | 1.015 | 9.8594 × | 1.015 |
1/320 | 3.4645 × | 1.009 | 4.8995 × | 1.009 |
1/640 | 1.7278 × | 1.004 | 2.4434 × | 1.004 |
, | Order | Order | ||
1/40 | 3.1908 × | 4.5125 × | ||
1/80 | 1.5587 × | 1.034 | 2.2044 × | 1.034 |
1/160 | 7.6515 × | 1.027 | 1.0821 × | 1.027 |
1/320 | 3.7717 × | 1.021 | 5.3340 × | 1.021 |
1/640 | 1.8668 × | 1.015 | 2.6400 × | 1.015 |
, | Order | Order | ||
1/40 | 2.7492 × | 3.8880 × | ||
1/80 | 1.3171 × | 1.061 | 1.8626 × | 1.062 |
1/160 | 6.3821 × | 1.045 | 9.0257 × | 1.045 |
1/320 | 3.1190 × | 1.033 | 4.4110 × | 1.033 |
1/640 | 1.5350 × | 1.023 | 2.1708 × | 1.023 |
, | Order | Order | ||
1/40 | 4.4875 × | 6.3463 × | ||
1/80 | 2.17887 × | 1.042 | 3.0813 × | 1.042 |
1/160 | 1.0650 × | 1.033 | 1.5061 × | 1.033 |
1/320 | 5.2380 × | 1.024 | 7.4077 × | 1.024 |
1/640 | 2.5912 × | 1.015 | 3.6646 × | 1.015 |
, | Order | Order | ||
1/40 | 5.3384 × | 7.5497 × | ||
1/80 | 2.5484 × | 1.067 | 3.6040 × | 1.067 |
1/160 | 1.2232 × | 1.059 | 1.7300 × | 1.059 |
1/320 | 5.9084 × | 1.050 | 8.3558 × | 1.050 |
1/640 | 2.8727 × | 1.040 | 4.0627 × | 1.040 |
, | Order | Order | ||
1/40 | 5.8816 × | 8.3178 × | ||
1/80 | 2.7960 × | 1.073 | 3.9541 × | 1.073 |
1/160 | 1.3360 × | 1.066 | 1.8893 × | 1.066 |
1/320 | 6.4204 × | 1.057 | 9.0799 × | 1.057 |
1/640 | 3.1052 × | 1.048 | 4.3915 × | 1.048 |
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Wang, Y.; Li, T.; Zhao, Y. The Finite Difference Method and Analysis for Simulating the Unsteady Generalized Maxwell Fluid with a Multi-Term Time Fractional Derivative. Fractal Fract. 2024, 8, 136. https://doi.org/10.3390/fractalfract8030136
Wang Y, Li T, Zhao Y. The Finite Difference Method and Analysis for Simulating the Unsteady Generalized Maxwell Fluid with a Multi-Term Time Fractional Derivative. Fractal and Fractional. 2024; 8(3):136. https://doi.org/10.3390/fractalfract8030136
Chicago/Turabian StyleWang, Yu, Tianzeng Li, and Yu Zhao. 2024. "The Finite Difference Method and Analysis for Simulating the Unsteady Generalized Maxwell Fluid with a Multi-Term Time Fractional Derivative" Fractal and Fractional 8, no. 3: 136. https://doi.org/10.3390/fractalfract8030136