Error estimates for time accurate wavelet based schemes for hyperbolic partial differential equations

International Journal of Wavelets, Multiresolution and Information Processing

Volumn 5, Issue 4, 2007, Pages 667-678

  Mehra, Mani ^a   Kumar, B V Rathish ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Hyperbolic equation; Multiresolution analysis; Time accurate schemes; Wavelets

Indexed keywords

CAUCHY PROBLEM; HYPERBOLIC EQUATION; SPECTRAL DECOMPOSITION; TIME ACCURATE SCHEMES;

BOUNDARY VALUE PROBLEMS; ERROR ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; WAVELET TRANSFORMS;

MULTIRESOLUTION ANALYSIS;

EID: 34447312187     PISSN: 02196913     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219691307001963     Document Type: Article

References (11)

1. W. Dahmen, A. J. Kurdila and P. Oswald (eds.), Multiscale Wavelet Methods for Partial Differential Equations (Academic Press, San Diego, CA, 1997).
2. J. Donea, A Taylor-Galerkin method for convective transport problems, Int. J. Numer. Method Eng. 20 (1984) 101-119.
3. A. Safjan and J. T. Oden, High-order Taylor Galerkin methods for linear hyperbolic systems, J. Comp. Phys. 120 (1995) 206-230.
4. B. V. Rathish Kumar and M. Mehra, Wavelet-Taylor Galerkin schemes for Parabolic and Hyperbolic problems, Int. J. Comput. Method. 5 1) (2005) 1-23.
5. B. V. Rathish Kumar and M. Mehra, Time accurate solution of Korteweg-de Vries equation using wavelet Galerkin method, Appl. Math. Comput. 162 (2005) 447-460.
6. M. Mehra and B. V. Rathish Kumar, Time-accurate solution of advection-diffusion problems by Wavelet Taylor Galerkin method, Comm. Numer. Method. Eng. 21 (2005) 313-326.
7. R, Trans. Amer. Math. Soc. 315(1) (1998) 69-87.
8. Y. Meyer, Wavelets and operators, in Analysis at Urbana I: Analysis in Function Spaces, London Mathematical Society Lecture Notes Series, Vol. 137 (Cambridge University Press, 1989), pp. 256-365.
9. K. Yoshida, Functional Analysis (Springer-Verlag, Berlin/Heidelberg/New York, 1974).
10. C. B. Jiang and M. Kawahara, The analysis of unsteady incompressible flows by a three-step finite element method, Int. J. Numer. Method. Fluids 16 (1993) 793-811.
11. W. Dahmen, S. Prossdorf, R. Schneider, Wavelet approximation methods for pseudidifferential equation I: Stability and convergence, Math. Zeit. 215 (1994) 583-620.