1United Arab Emirates University, Faculty of Sciences, Mathematical Sciences Department, P.O. Box 17551, Al Ain, UAE. E-mail: hakca@uaeu.ac.ae
2King Fahd University of Petroleum and Minerals, Department of Mathematical Science, Dhahran 31261, Saudi Arabia.
3Department of Mathematics & Statistics, College of Science, Sultan Qaboos University, Sultanate of Oman. E-mail: vcovachev@hotmail.com
AMS subject classification: 42C40, 34B05, 65T60.
We study historical development of wavelets and introduce basic definitions and formulations. Wavelets are mathematical tools that cut up data or functions or operators into different frequency components, and then study each component with a resolution matching to its scale. We discuss different approaches of using wavelets in the solution of boundary value problems for ordinary differential equations. We also introduce convenient wavelet representations for the derivatives for certain functions. A wavelet network is a network combining the idea of the feedforward neural networks and the wavelet decomposition. Recent developments and wavelet network algorithm are discussed.
Wavelet, networks, multiresolution analysis, orthonormal basis, Fourier analysis, boundary value problems
