Survey on Wavelet Transform and Application in ODE and Wavelet Networks
Haydar Akça, Mohammed H. Al-Lail, King Fahd · 2006
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 feed-forward neural networks and the wavelet decomposition. Recent developments and wavelet network algorithm are discussed. AMS subject classification: 42C40, 34B05, 65T60.