Multiquadric approximation scheme on the numerical solution of delay differential systems of neutral type

Mathematical and Computer Modelling

Volumn 49, Issue 1-2, 2009, Pages 234-241

  Karimi Vanani, S ^a   Aminataei, A ^a  

^a K N TOOSI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Delay differential systems; Error analysis; Multiquadric approximation scheme; Neutral delay differential systems; Run time of computations; Stability of the method

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; POLYNOMIAL APPROXIMATION; SYSTEM STABILITY;

APPROXIMATION SCHEMES; DATA POINTS; DELAY DIFFERENTIAL SYSTEMS; DIFFERENTIAL SYSTEMS; ERROR ESTIMATIONS; HIGH ACCURACIES; MULTIQUADRIC; MULTIQUADRIC APPROXIMATION SCHEME; NEUTRAL DELAY DIFFERENTIAL SYSTEMS; NEUTRAL TYPES; NUMERICAL RESULTS; NUMERICAL SOLUTIONS; RUN TIME OF COMPUTATIONS; RUN TIMES;

NUMERICAL METHODS;

EID: 55549132926     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2008.03.016     Document Type: Article

References (18)

1. Hale J., and Verduyn Lunel S.M. Introduction to Functional Differential Equations (1993), Springer-Verlag, New York
2. Kolmanovskii V., and Myshkis A. Applied Theory of Functional Differential Equations (1992), Kluwer Academic Publishers, Dordrecht
3. Salamon D. Control and Observation of Neutral Systems (1984), Pitman Advanced Publishing Program, Boston, MA
4. Hardy R.L. Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res. 76 (1971) 1905
5. Hardy R.L. Theory and applications of the multiquadric bi-harmonic method: 20 years of discovery. Comput. Math. Appl. 19 8-9 (1990) 163
6. Franke R. Scattered data interpolation: Tests of some methods. Math. Comput. 38 (1971) 181
7. Zerroukut M., Power H., and Chen C.S. A numerical method for heat transfer problems using collocation and radial basis functions. Internat. J. Numer. Methods Engrg. 42 (1998) 1263
8. Mai-Duy N., and Tran-Cong T. Numerical solution of differential equations using multiquadric radial basis function networks. Neutral Networks. 14 (2001) 185
9. Aminataei A., and Mazarei M.M. Numerical solution of elliptic partial differential equarions using direct and indirect radial basis function networks. Euro. J. Scien. Res. 2 2 (2005) 5
10. Micchelli C.A. Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constr. Approx. 2 (1986) 11
11. Madych W.R., and Nelson S.A. Multivariable interpolation and conditionally positive definite functions II. Math. Comp. 54 (1990) 211
12. Kansa E.J. Multiquadrics - A scattered data approximation scheme with applications to computational fluid dynamics - I. Surface approximations and partial derivative estimates. Comput. Math. Appl. 19 8-9 (1990) 127
13. Kansa E.J. Multiquadrics - A scattered data approximation scheme with applications to computational fluid dynamics - II. Solutions to hyperbolic, parabolic and elliptic partial differential equations. Comput. Math. Appl. 19 8-9 (1990) 147
14. Aminataei A., and Sharan M. Using multiquadric method in the numerical solution of ODEs with a singularity point and PDEs in one and two dimensions. Euro. J. Scien. Res. 10 2 (2005) 19
15. Madych W.R. Miscellaneous error bounds for multiquadric and related interpolants. Comput. Math. Appl. 24 12 (1992) 121
16. Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. Spectral Method in Fluid Dynamics. Springer Series in Computational Physics (1988), Springer-Verlag, New York
17. Constantinides A. Applied Numerical Methods with Personal Computers (1987), McGraw-Hill, New York
18. Bellen A., and Zennaro M. Numerical Methods for Delay Differential Equations, Numerical Mathematics and Scientific Computations Series (2003), Oxford University Press, Oxford