A general spline differential quadrature method based on quasi-interpolation

Journal of Computational and Applied Mathematics

Volumn 275, Issue , 2015, Pages 465-479

  Barrera, D ^a   Gonzalez P ^a   Ibanez F ^b   Ibanez M J ^a  

^a UNIVERSITY OF GRANADA   (Spain)

^b Grupo Sacyr y Vallehermoso   (Spain)

Author keywords

B splines; Differential quadrature method; Differential quasi interpolants; Discrete quasi interpolants; Error estimates; Interpolation

Indexed keywords

DIFFERENTIATION (CALCULUS); NUMERICAL METHODS;

B SPLINES; DIFFERENTIAL QUADRATURE METHODS; DISCRETE QUASI-INTERPOLANTS; ERROR ESTIMATES; INTERPOLANTS;

INTERPOLATION;

EID: 84908154152     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2014.02.006     Document Type: Article

References (25)

1. C.W. Bert, and M. Malik Differential quadrature method in computational mechanics: a review Appl. Rev. 49 1996 1 27
2. C. Shu Differential Quadrature and its Applications in Engineering 2000 Springer-Verlag
3. C.K. Chui Multivariate Splines CBMS-NSF Regional Conference Series in Applied Mathematics vol. 54 1988 SIAM Philadelphia
4. L.L. Schumaker Spline Functions. Basic Theory 1981 John Wiley & Sons New York
5. Q. Guo, and H. Zhong Non-linear vibration analysis of beams by a spline-based differential quadrature method J. Sound Vib. 269 2004 413 420
6. H. Zhong Spline-based differential quadrature for fourth order differencial equations and its applications to Kirchhoff plates Appl. Math. Model. 28 2004 353 366
7. H. Zong, and M. Lan Solution of nonlinear initial-value problems by the spline-based differential quadrature method J. Sound Vib. 296 2006 908 918
8. W. Dahmen, T.N.T. Goodman, and C.A. Micchelli Compactly supported fundamental functions for spline interpolation Numer. Math. 52 1988 639 664
9. C.A. Micchelli Banded matrices with banded inverses J. Comput. Appl. Math. 41 1992 281 300
10. D.X. Qi A class of local explicit many-knot spline interpolation schemes, MRC Technical Summary Report 2238 1981
11. Z 2 Numer. Math. 70 1995 331 351
12. I.J. Schoenberg Contributions to the problem of approximation of equidistant data by analytical functions, Parts A and B Quart. Appl. Math. IV 1 1946 45 99 pp. 112-141
13. I.J. Schoenberg Cadinal Spline Interpolation 1973 SIAM
14. C. de Boor A Practical Guide to Splines 2001 Springer-Verlag New York
15. D. Barrera, M.J. Ibáñez, and P. Sablonnière Near-best discrete quasi-interpolants on uniform and nonuniform partitions A. Cohen, J.-L. Merrien, L.L. Schumaker, Curve and Surface Fitting: Saint-Malo 2002 2003 Nashboro Press Brentwood 31 40
16. D. Barrera, M.J. Ibáñez, P. Sablonnière, and D. Sbibih Near minimally normed spline quasi-interpolants on uniform partitions J. Comput. Appl. Math. 181 2005 211 233
17. R.A. DeVore, and G.G. Lorentz Constructive Approximation 1993 Springer-Verlag Berlin
18. J. Hoschek, and D. Lasser Fundamentals of Computer Aided Geometric Design 1993 A. K. Peters Wellesley, Massachussets
19. P. Sablonnière, Spline quasi-interpolants on uniform partitions, Preprint IRMAR 00-38, 2000 (in Spanish).
20. P.L. Butzer, M. Schmidt, E.L. Stark, and L. Vogt Central factorial numbers; their main properties and some applications Numer. Funct. Anal. Optim. 10 5-6 1989 419 488
21. D. Barrera-Rosillo, and F. Ibáñez-Pérez Compactly Supported Fundamental Functions for Spline-Based Differential Quadrature, III European Conference on Computational Mechanics 2006 Springer-Verlag The Netherlands
22. G.M. Phillips Interpolation and Approximation by Polynomials 2003 Springer-Verlag New-York
23. M.J. Ibáñez Pérez, Quasi-interpolantes spline discretos de norma casi mínima. Teoría y aplicaciones, Doctoral Dissertation, University of Granada, 2003.
24. M.J. Ibáñez Pérez On Chebyshev-type discrete quasi-interpolants Math. Comput. Simul. 77 2008 21 227
25. M.A. Fortes, M.J. Ibáñez, and M.L. Rodríguez On Chebyshev-type integral quasi-interpolation operators Math. Comput. Simul. 79 2009 3478 3491