On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations
Abstract
:1. Introduction
2. Stability of DS
3. Applications
4. Numerical Results
4.1. One-Dimensional Problem
4.2. Two-Dimensional Problem
5. Conclusions
- In this paper, the absolutely stable DS of a first order of accuracy for the approximate solution of the DPDE in a Hilbert space was presented. The theorem on the stability of this difference scheme was proven. In practice, stability estimates for the solutions of three-step difference schemes for different types of delay partial differential equations were obtained. Numerical results were given.
- The mixed problem for the one-dimensional DPDE with the Dirichlet condition was studied in [41]. The first and second order of accuracy DSs for the numerical solution of this problem were presented. The illustrative numerical results were provided. We are interested in studying absolutely stable DSs of a high order of accuracy of the approximate solution of the initial value problem (1) for the DPDE in a Hilbert space.
- Applying this approach and the method [30], we could study the existence and uniqueness of a bounded solution of the initial value problem for the semilinear DPDE:
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Sample Availability: Samples of the compounds are available from the authors. |
l/N,M | 20,20 | 40,40 | 80,80 | |
---|---|---|---|---|
0.0141 | 0.0068 | 0.0040 | ||
0.0559 | 0.0322 | 0.0172 | ||
0.1346 | 0.0746 | 0.0392 | ||
0.2011 | 0.1011 | 0.0561 |
l/N,M | 10,10 | 20,20 | 40,40 | |
---|---|---|---|---|
0.0370 | 0.0162 | 0.0083 | ||
0.0840 | 0.0456 | 0.0236 | ||
0.1028 | 0.0543 | 0.0276 | ||
0.1008 | 0.0521 | 0.0261 |
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Ashyralyev, A.; Hınçal, E.; Ibrahim, S. On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations. Symmetry 2020, 12, 1033. https://doi.org/10.3390/sym12061033
Ashyralyev A, Hınçal E, Ibrahim S. On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations. Symmetry. 2020; 12(6):1033. https://doi.org/10.3390/sym12061033
Chicago/Turabian StyleAshyralyev, Allaberen, Evren Hınçal, and Suleiman Ibrahim. 2020. "On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations" Symmetry 12, no. 6: 1033. https://doi.org/10.3390/sym12061033