Accession Number : ADA309649

Title :   A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method.

Descriptive Note : Contractor rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Jameson, Leland

PDF Url : ADA309649

Report Date : MAY 1996

Pagination or Media Count : 43

Abstract : Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebyshev grid and this grid is refined locally based on wavelet analysis.

Descriptors :   *FINITE DIFFERENCE THEORY, *NUMERICAL METHODS AND PROCEDURES, OPTIMIZATION, GRIDS, ACCURACY, APPROXIMATION(MATHEMATICS), ERROR ANALYSIS, POLYNOMIALS, INTERPOLATION, ADAPTIVE SYSTEMS, OPERATORS(MATHEMATICS), LAGRANGIAN FUNCTIONS, ALGEBRAIC FUNCTIONS, CHEBYSHEV FUNCTIONS.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE