B-Spline Solution and the Chaotic Dynamics of Troesch's Problem

• Authors: H. Caglar , N. Caglar , M. Ozer
• Languages of publication: EN

Abstracts

EN

A B-spline method is presented for solving the Troesch problem. The numerical approximations to the solution are calculated and then their behavior is studied and commenced. The chaotic dynamics exhibited by the solutions of Troesch's problem as they were derived by the decomposition method approximation are examined and an approximate critical value for the parameter λ is introduced also in this study. For the parameter value slightly less than λ ≈ 2.2, the solutions begin to show successive bifurcations, finally entering chaotic regimes at higher λ values. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where the first bifurcation occurs.

Keywords

EN

05.45.Pq; 02.60.-x; 02.60.Lj

Discipline

• 05.45.Pq: Numerical simulations of chaotic systems
• 02.60.Lj: Ordinary and partial differential equations; boundary value problems
• 02.60.-x: Numerical approximation and analysis

• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 125
• Issue: 2
• Pages: 554-560

Dates

published

2014-02

Contributors

author

H. Caglar

• Istanbul Kultur University, Department of Mathematics-Computer, Istanbul, Turkey

author

N. Caglar

• Istanbul Kultur University, Faculty of Economic and Administrative Science, Istanbul, Turkey

author

M. Ozer

• Istanbul Kultur University, Department of Physics, Istanbul, Turkey

References

• 1. J.P. Chiou, T.Y. Na, doi: 10.1016/0021-9991(75)90080-7, J. Comput. Phys. 19, 311 (1975)
• 2. J. Lang, A. Walter, doi: 10.1016/0899-8248(92)90004-R, Impact Comput. Sci. Eng. 4, 269 (1992)
• 3. E. Deeba, S.A. Khuri, S. Xie, doi: 10.1006/jcph.2000.6452, J. Comput. Phys. 159, 125 (2000)
• 4. X. Feng, L. Mei, G. He, doi: 10.1016/j.amc.2006.11.161, Appl. Math. Comput. 189, 500 (2007)
• 5. S.A. Khuri, doi: 10.1080/0020716022000009228, Int. J. Comp. Math. 80, 493 (2003)
• 6. S.H. Chang, I.L. Chang, doi: 10.1016/j.amc.2007.05.026, Appl. Math. Comput. 195, 799 (2008)
• 7. S. Momani, S. Abuasad, Z. Odibat, doi: 10.1016/j.amc.2006.05.138, Appl. Math. Comput. 183, 1351 (2006)
• 8. E. Babolian, Sh. Javadi, doi: 10.1016/S0096-3003(03)00629-5, Appl. Math. Comput. 153, 253 (2004)
• 9. Y. Lin, J.A. Enszer, M.A. Stadtherr, doi: 10.1016/j.compchemeng.2007.08.013, Comput. Chem. Eng. 32, 1714 (2008)
• 10. M.R. Scott, H.A. Watts, in: Numerical Methods for Differential Systems, Eds. L. Lapidus, W.E. Schiesser, Academic Press, New York 1976, p. 197
• 11. M.R. Scott, H.A. Watts, SIAM J. Numer. Anal. 14, 40 (1977)
• 12. M.R. Scott, W.H. Vandevender, doi: 10.1016/0096-3003(75)90033-8, Appl. Math. Comput. 1, 187 (1975)
• 13. J.R. Cash, F. Mazzia, doi: 10.1016/j.cam.2005.01.016, J. Comput. Appl. Math. 184, 362 (2005)
• 14. H. Caglar, N. Caglar, M. Ozer, A. Valaristos, A.N. Anagnostopoulos, doi: 10.1080/00207160802545882, Int. J. Comp. Math. 87, 1885 (2010)
• 15. S.M. Roberts, J.S. Shipman, doi: 10.1016/0021-9991(76)90026-7, J. Comput. Phys. 21, 291 (1976)
• 16. M. Kubicek, V. Hlavacek, doi: 10.1016/0021-9991(75)90066-2, J. Comput. Phys. 17, 95 (1975)
• 17. C. de Boor, A Practical Guide to Splines, Springer-Verlag, New York 1978
• 18. R. Fletcher, Practical Methods of Optimization, Wiley, Southern Gate 1987
• 19. H. Caglar, N. Caglar, M. Ozer, A. Valaristos, A.N. Miliou, A.N. Anagnostopoulos, doi: 10.1016/j.na.2008.11.091, Nonlinear Anal. Theor. Meth. Appl. 71, e672 (2009)

Identifiers

DOI

10.12693/APhysPolA.125.554