Operational tau approximation for neutral delay differential systems

Journal of Applied Sciences

Volumn 11, Issue 14, 2011, Pages 2585-2591

  Sedighi Hafshejani, J ^a   Karimi Vanani, S ^a   Esmaily, J ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Delay differential equations; Neutral delay differential systems; Spectral methods; Tau method

Indexed keywords

EID: 79958279890     PISSN: 18125654     EISSN: 18125662     Source Type: Journal    
DOI: 10.3923/jas.2011.2585.2591     Document Type: Article

References (20)

1. Doha, E.H. and W.M. Abd-Elhameed, 2005. Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method. J. Comput. Applied Math., 181: 24-45.
2. El-Daou, M.K. and H.G. Khajah, 1997. Iterated solutions of linear operator equations with the Tau method. Math. Comput., 66: 207-213.
3. Garcia-Olivares, A., 2002. Analytical approximants of time-dependent partial differential equations with Tau methods. Math. Comput. Simul., 61: 35-45.
4. Ghafarian, P., M.T. Zamanian and T. Haghroosta, 2011. Design of barotropic spectral model for predicting of vorticity field. Res. J. Environ. Sci., 5: 386-393.
5. Hale, J. and S.M. Verduyn Lunel, 1993. Introduction to Functional Differential Equations. Springer, New York, USA., ISBN-13: 9780387940762, pp: 447.
6. Kolmanovskii, V.B. and A.D. Myshkis, 1992. Applied Theory of Functional Differential Equations. Kluwer Academic Publishers, Dordrecht, The Netherlands, ISBN-13: 9780792320135, pp: 234.
7. Kong, W. and X. Wu, 2009. Chebyshev tau matrix method for Poisson-type equations in irregular domain. J. Comput. Applied Math., 228: 158-167.
8. Lanczos, C, 1938. Trigonometric interpolation of empirical and analytic functions. J. Math. Phys., 17: 123-199.
9. Liu, K.M. and C.K. Pan, 1999. The automatic solution to systems of ordinary differential equations by the Tau method. Comput. Math. Appl, 38: 197-210.
10. Matos, I., M.I. Rodrigues and P.B. Vasconcelos, 2004. New implementation of the Tau method for PDEs. I. Comput. Applied Math., 164-165: 555-567.
11. Parand, K. and M. Razzaghi, 2004. Rational Chebyshev Tau method for solving volterra's population model. Applied Math. Comput., 149: 893-900.
12. Pour-Mahmoud, I., M.Y. Rahimi-Ardabili and S. Shahmorad, 2005. Numerical solution of the system of Fredholm integro-differential equations by the Tau method. AppliedMath. Comput, 168: 465-478.
13. Rahimi-Ardabili, M.Y. and S. Shahmorad, 2007. Iterative numerical solution of non-linear integro-differential equations by the Tau method. Applied Math. Comput, 193: 514-522.
14. Rao, T.P., K.S. Rao and C.L. Usha, 2011. Stochastic modeling of blood glucose levels in type-2 diabetes mellirus. Asian I. Mathe. Stat., 4: 56-65.
15. Salamon, D., 1984. Control and Observation of Neutral Systems. Pitman Advanced Publishing Program, Boston, MA., USA., ISBN-13: 9780273086185, pp: 204.
16. Taiwo, O.A. and A. Abubakar, 2011. An application method for the solution of second order non linear ordinary differential equations by Chebyshev polynomials. Asian I. Applied Sci., 4: 255-262.
17. Taiwo, O.A. and O.S. Odetunde, 2010. On the numerical approximation of delay differential equations by a decomposition method. Asian I. Math. Stat, 3: 237-243.
18. Tasci, F., 2003. On the approximative solution of boundary value problems by collocation. I. Applied Sci., 3: 210-215.
19. Vanani, S.K. and A. Aminataei, 2009. Multiquadric approximation scheme on the numerical solution of delay differential systems of neutral type. Math. Comput. Modell., 49: 234-241.
20. Vanani, S.K. and A. Aminataei, 2010. On the numerical solution of delay differential systems. J. Applied Funct. Anal, 5: 169-176.