Segmented Tau approximation for test neutral functional differential equations

Applied Mathematics and Computation

Volumn 187, Issue 2, 2007, Pages 725-740

  Cordero, Luis F ^a   Escalante, René ^b  

^a UNIVERSIDAD DE CARABOBO   (Venezuela)

^b UNIVERSIDAD SIMÓN BOLÍVAR   (Venezuela)

Author keywords

Functional differential equations; Neutral delay differential equations; Polynomial approximation; Step by step Tau method approximation

Indexed keywords

COMPUTATIONAL COMPLEXITY; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; OPTIMIZATION; POLYNOMIAL APPROXIMATION;

FUNCTIONAL DIFFERENTIAL EQUATIONS; NEUTRAL DELAY DIFFERENTIAL EQUATIONS; STEP BY STEP TAU METHOD APPROXIMATION;

COMPUTATIONAL METHODS;

EID: 34247263187     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.08.085     Document Type: Article

References (39)

1. Kappel F., and Kunisch K. Spline approximations for neutral functional differential equations. SIAM J. Numer. Anal. 18 (1981) 1058-1080
2. Z. Jackiewicz, E. Lo, The numerical integration of neutral functional-differential equations by fully implicit one-step methods, Technical Report No. 129, Arizona State University, Mathematics Department, 1991.
3. Ito K., Tran H., and Manitius A. A fully-discrete spectral method for delay differential equations. SIAM J. Numer. Anal. 28 (1991) 1121-1140
4. C. Paul, A test set of functional differential equations, Technical Report No. 243, University of Manchester, Manchester Centre for Computational Mathematics, Numerical Analysis Reports, 1994.
5. L.F. Cordero, R. Escalante, Segmented Tau approximation for a parametric nonlinear neutral differential equation, submitted for publication.
6. Khajah H. Tau method treatment of a delayed negative feedback equation. Comput. Math. Appl. 49 (2005) 1767-1772
7. Khajah H., and Ortiz E. On a differential-delay equation arising in number theory. Appl. Numer. Math. 21 (1996) 431-437
8. D. Gottlieb, Orszag, Numerical analysis of spectral methods: theory and applications, in: CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1977.
9. Banks H., and Kappel F. Spline approximations for functional differential equations. J. Differen. Equat. 34 (1979) 496-522
10. Ito K., and Teglas R. Legendre-tau approximations for functional differential equations. SIAM J. Control Optim. 24 (1986) 737-759
11. C. Baker, C. Paul, D. Willé, A bibliography on the numerical solution of delay differential equations, Technical Report NA No. 269, University of Manchester, Department of Mathematics, Manchester Centre for Computational Mathematics, 1995.
12. Dib Y., Maroun M., and Raffoul Y. Periodicity and stability in neutral nonlinear differential equations with functional delay. Electron. J. Differen. Equat. 142 (2005) 1-11
13. Bellen A., and Zennaro M. Numerical Methods for Delay Differential Equations (2003), Oxford University Press, New York
14. Diekmann O., van Gils S., Lunel S.V., and Walther H.-O. Delay Equations (1995), Springer, New York
15. Lanczos C. Trigonometric interpolation of empirical and analytical functions. J. Math. Phys. 17 (1938) 123-199
16. Lanczos C. Introduction, Tables of Chebyshev polynomials. Appl. Math. Ser. U.S. Bur. Stand., 9 (1952), Government Printing Office, Washington
17. Lanczos C. Applied Analysis (1956), Prentice-Hall Inc., New Jersey
18. Luke Y. The Special Functions and their Approximations vol. II (1969), Academic Press, New York
19. Lanczos C. Legendre versus Chebyshev polynomials. In: Miller J. (Ed). Topics in Numerical Analysis (1973), Academic Press, New York
20. Ortiz E., and Dinh A.P.N. An error analysis of the Tau method for a class of singularly perturbed problems for differential equations. Math. Methods Appl. Sci. 6 (1984) 457-466
21. Ortiz E., and Dinh A.P.N. On the convergence of the Tau method for nonlinear differential equations of Riccati's type. Nonlinear Anal. Theory Methods Appl. 9 (1985) 53-60
22. Ortiz E. The Tau method. SIAM J. Numer. Anal. 6 (1969) 480-492
23. Freilich J., and Ortiz E. Numerical solution of systems of ordinary differential equations with the tau method: an error analysis. Math. Comput. 39 (1982) 467-479
24. Onumanyi P., and Ortiz E. Numerical solution of stiff and singularly perturbed boundary value problems with a segmented-adaptive formulation of the Tau method. Math. Comput. 43 167 (1984) 189-203
25. Ortiz E., and Samara H. An operational approach to the Tau method for the numerical solution of non-linear differential equations. Computing 27 (1981) 15-25
26. Chaves T., and Ortiz E. On the numerical solution of two point boundary value problems for linear differential equations. Z. Angew. Math. Mech. 48 (1968) 415-418
27. Liu K., and Ortiz E. Tau method approximate solution of high-order differential eigenvalue problems defined in the complex plane, with an application to Orr-Sommerfeld stability equation. Commun. Appl. Numer. Methods 3 (1987) 187-194
28. Ortiz E., and Samara H. Numerical solution of differential eigenvalue problems with an operational approach to the Tau method. Computing 31 (1983) 95-103
29. Namasivayam S., and Ortiz E. Best approximation and the numerical solution of partial differential equations with the Tau method. Port. Math. 40 (1985) 97-119
30. El-Daou M., and Ortiz E. The Tau method as an analytic tool in the discussion of equivalence results across numerical methods. Computing 60 4 (1998) 365-376
31. Ortiz E., and Dinh A.P.N. Some remarks on structural relations between the Tau method and the finite element method. Comput. Math. Appl. 33 4 (1997) 105-113
32. Ortiz E. Step by step Tau method - Part I: Piecewise polynomial approximations. Comput. Math. Appl. 1 (1975) 381-392
33. Escalante R. Parallel strategies for the step by step Tau method. Appl. Math. Comput. 137 (2003) 277-292
34. E. Ortiz, W. Purser, F. Rodriguez-Cañizares, Automation of the Tau method, Technical Report NAS 01-72, Imperial College, 1972 (Presented to the Conference on Numerical Analysis organized by the Royal Irish Academy, Dublin, 1972).
35. C. Baker, J. Butcher, C. Paul, Experience of STRIDE applied to delay differential equations, Technical Report NA No. 208, University of Manchester, Department of Mathematics, Manchester Centre for Computational Mathematics, 1992.
36. Shampine L., and Thompson S. Solving DDEs in MATLAB. Appl. Numer. Math. 37 (2001) 441-458
37. Shampine L., Gladwell I., and Thompson S. Solving ODEs with MATLAB (2003), Cambridge University Press, Cambridge, UK
38. Butcher J. The adaptation of STRIDE to delay differential equations. Appl. Numer. Math. 9 (1992) 415-425
39. El'sgol'ts L., and Norkin S. Introduction to the Theory and Applications of Differential Equations with Deviating Arguments (1973), Academic Press, New York