scholarly journals Higher-order Haar wavelet method for vibration analysis of nanobeams

2020 ◽  
Vol 25 ◽  
pp. 101290 ◽  
Author(s):  
J. Majak ◽  
B. Shvartsman ◽  
M. Ratas ◽  
D. Bassir ◽  
M. Pohlak ◽  
...  
Keyword(s):  
Vibration Analysis ◽  
Haar Wavelet ◽  
Higher Order ◽  
Wavelet Method ◽  
Haar Wavelet Method

Application of HOHWM for Vibration Analysis of Nanobeams

2019 ◽  
Vol 799 ◽  
pp. 230-235 ◽  
Author(s):  
Maarjus Kirs ◽  
Martin Eerme ◽  
David Bassir ◽  
Ernst Tungel
Keyword(s):  
Rate Of Convergence ◽  
Vibration Analysis ◽  
Absolute Error ◽  
Haar Wavelet ◽  
Higher Order ◽  
Wavelet Method ◽  
Expansion Parameter ◽  
Haar Wavelet Method ◽  
Collocation Points ◽  
The Absolute

The higher order Haar wavelet method (HOHWM) introduced recently by workgroup is utilized for vibration analysis of nanobeams. The results obtained are compared with widely used Haar wavelet method. It has been observed that the absolute error has been reduced several magnitudes depending on number of collocation points used and the numerical rate of convergence was improved from two to four. These results are obtained in the case of the simplest higher order approach where expansion parameter k is equal to one. The complexity issues of the HOHWM are discussed.

scholarly journals Higher Order Haar Wavelet Method for Solving Differential Equations

2020 ◽  
Author(s):  
Jüri Majak ◽  
Mart Ratas ◽  
Kristo Karjust ◽  
Boris Shvartsman
Keyword(s):  
Differential Equations ◽  
Computational Cost ◽  
Haar Wavelet ◽  
Higher Order ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Convergence Results ◽  
Key Characteristics ◽  
Parameter Values ◽  
Excellent Accuracy

The study is focused on the development, adaption and evaluation of the higher order Haar wavelet method (HOHWM) for solving differential equations. Accuracy and computational complexity are two measurable key characteristics of any numerical method. The HOHWM introduced recently by authors as an improvement of the widely used Haar wavelet method (HWM) has shown excellent accuracy and convergence results in the case of all model problems studied. The practical value of the proposed HOHWM approach is that it allows reduction of the computational cost by several magnitudes as compared to HWM, depending on the mesh and the method parameter values used.

New higher order Haar wavelet method: Application to FGM structures

2018 ◽  
Vol 201 ◽  
pp. 72-78 ◽  
Author(s):  
J. Majak ◽  
M. Pohlak ◽  
K. Karjust ◽  
M. Eerme ◽  
J. Kurnitski ◽  
...  
Keyword(s):  
Haar Wavelet ◽  
Higher Order ◽  
Wavelet Method ◽  
Haar Wavelet Method

Haar wavelet method for vibration analysis of nanobeams

2016 ◽  
Vol 2 (1) ◽  
pp. 20-28 ◽  
Author(s):  
M. Kirs ◽  
M. Mikola ◽  
A. Haavajõe ◽  
E. Õunapuu ◽  
B. Shvartsman ◽  
...  
Keyword(s):  
Vibration Analysis ◽  
Haar Wavelet ◽  
Wavelet Method ◽  
Haar Wavelet Method
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