Applications of Taylor Collocation Method and Lambert W Function to the Systems of Delay Differential Equations

Abstract

In this paper, the systems of delay differential equations with initial conditions are solved by using Taylor Collocation Method and Lambert W Function and we tried to show the appropriate method by comparing the solution process of the system of these equations. All numerical computations have been performed on the computer algebraic system Matlab.

Keywords

• Delay differential equations, Taylor collocation method, Lambert function.

References

1. Asl F. M., Ulsoy A. G., Analysis of a system of linear delay differential equations, ASME J. Dyn. Syst. Meas. Cont., 125(2), 215-223 (2003).
2. Asl F. M., Ulsoy A. G., Analytical solution of a system of homogeneous delay differential equations via the Lambert function, Proc. Americ. Cont. Conf., Chicago, Illinois June (2000).
3. Bellen A., Zennaro M., Numerical methods for delay differential equations. London: Clarendon Press; (2003).
4. Bildik N., Aygun M., Gecikmeli diferansiyel denklemlerin farkli tipteki numerik cozumleri, Celal Bayar Universitesi, Fen Bilimleri Enstitusu, Yuksek Lisans Tezi, (2012).
5. Corless, Robert M., et al. ”On the Lambert W function.” Advances in Computational Mathematics 5.1 (1996): 329-359.
6. Gokmen E., Sezer M., Taylor collocation method for systems of high-order linear differential-difference equations with variable coefficients, Ain Shams Eng. J., 4, 117-125 (2013).
7. Bellman R. E., Cooke K. L., Differential-Difference Equations, Academic Press, (1963).
8. Ilhan E, Diferansiyel denklemlerin varyasyonel iterasyon metodu ile yaklasik analitik cozumleri, Ahi Evran Universitesi, Fen Bilimleri Enstitusu, Yuksek Lisans Tezi, (2011).

9. Gulsu, M., Gürbüz, B., Öztürk, Y.,Sezer, M. (2011). Laguerre polynomial approach for solving linear delay difference equations. Applied Mathematics and Computation, 217(15), 6765-6776.
10. Sezer, Mehmet, and Ays¸egul Akyüz-Das¸cioğlu. ”A Taylor method for numerical solution of generalized pantograph equations with linear functional argument.” Journal of Computational and Applied Mathematics 200.1 (2007): 217-225.
11. Sezer, Mehmet, Salih Yalcinbas¸, and Mustafa Gulsu. ”A Taylor polynomial approach for solving generalized pantograph equations with nonhomogenous term.” International Journal of Computer Mathematics 85.7 (2008): 1055-1063.
12. Yi S., Nelson P.W., Ulsoy G.A., Analysis of systems of linear delay differential equations using the matrix Lambert function and the Laplace transformation, Automatica, 5 January (2006).
13. Yi S., Nelson P.W., Ulsoy G.A., Delay differential equations via the matrix Lambert W function and bifurcation analysis: Application to machine tool chatter, Math.l Biosci. Eng., 4(2), 355-368, (2007).
14. Yi, S., P. W. Nelson, and A. G. Ulsoy. ”Eigenvalue assignment via the Lambert W function for control of time-delay systems.” Journal of Vibration and Control 16.7-8 (2010): 961-982.