Abstract: In this paper, we have proposed a Haar wavelet quasilinearization
method to solve the well known Blasius equation. The
method is based on the uniform Haar wavelet operational matrix
defined over the interval [0, 1]. In this method, we have proposed the
transformation for converting the problem on a fixed computational
domain. The Blasius equation arises in the various boundary layer
problems of hydrodynamics and in fluid mechanics of laminar
viscous flows. Quasi-linearization is iterative process but our
proposed technique gives excellent numerical results with quasilinearization
for solving nonlinear differential equations without any
iteration on selecting collocation points by Haar wavelets. We have
solved Blasius equation for 1≤α ≤ 2 and the numerical results are
compared with the available results in literature. Finally, we
conclude that proposed method is a promising tool for solving the
well known nonlinear Blasius equation.
Abstract: Electrocardiogram (ECG) is considered to be the
backbone of cardiology. ECG is composed of P, QRS & T waves and
information related to cardiac diseases can be extracted from the
intervals and amplitudes of these waves. The first step in extracting
ECG features starts from the accurate detection of R peaks in the
QRS complex. We have developed a robust R wave detector using
wavelets. The wavelets used for detection are Daubechies and
Symmetric. The method does not require any preprocessing therefore,
only needs the ECG correct recordings while implementing the
detection. The database has been collected from MIT-BIH arrhythmia
database and the signals from Lead-II have been analyzed. MatLab
7.0 has been used to develop the algorithm. The ECG signal under
test has been decomposed to the required level using the selected
wavelet and the selection of detail coefficient d4 has been done based
on energy, frequency and cross-correlation analysis of decomposition
structure of ECG signal. The robustness of the method is apparent
from the obtained results.