Construction of the matched multiple knot B-spline wavelets on a bounded interval

Abstract

In order to solve a boundary value problem using Galerkin's method, the selection of basis functions plays a crucial rule. When the solution of a boundary value problem is not enough smooth or the domain is irregular, multiple knot B-spline wavelets (MKBSWs) with locally compact support are appropriate basis functions. However, to have globally continuous basis functions, a matching across the subdomain interfaces is required. In other words, MKBSWs that are non-zero in the interelement boundaries should be matched. In this paper, we present the primal and dual matched multiple knot B-spline scaling and wavelet functions whose main properties of smoothness and biorthogonality are kept.

Keywords:

• multiple knot B-spline
• wavelet
• matching

2010 AMS Subject Classifications:

• 41A15
• 65T60
• 65D07
• 65M60

Acknowledgements

The writers are very grateful to Dr H. Fathi, the faculty member of Vali-e-Asr University of Rafsanjan, Iran, for his kind cooperation in reading the manuscript of the article and providing linguistic hints.