Convergence theorem for the Haar wavelet based discretization method

J Majak, BS Shvartsman, M Kirs, M Pohlak… - Composite …, 2015 - Elsevier
The accuracy issues of Haar wavelet method are studied. The order of convergence as well
as error bound of the Haar wavelet method is derived for general n th order ODE. The …

New higher order Haar wavelet method: Application to FGM structures

J Majak, M Pohlak, K Karjust, M Eerme, J Kurnitski… - Composite …, 2018 - Elsevier
A new higher order Haar wavelet method (HOHWM) has been developed for solving
differential and integro-differential equations. Generalized approach has been proposed for …

Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schrödinger Equation with Energy and Mass Conversion

X Liu, M Ahsan, M Ahmad, M Nisar, X Liu, I Ahmad… - Energies, 2021 - mdpi.com
This article is concerned with the numerical solution of nonlinear hyperbolic Schr o¨ dinger
equations (NHSEs) via an efficient Haar wavelet collocation method (HWCM). The time …

[HTML][HTML] A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations

I Aziz, F Khan - Journal of Computational and Applied Mathematics, 2014 - Elsevier
A new numerical method based on Haar wavelet is proposed for two-dimensional nonlinear
Fredholm, Volterra and Volterra–Fredholm integral equations of first and second kind. The …

[HTML][HTML] On the accuracy of the Haar wavelet discretization method

J Majak, B Shvartsman, K Karjust, M Mikola… - Composites Part B …, 2015 - Elsevier
Current study contains adaption of Haar wavelet discretization method (HWDM) for FG
beams and its accuracy estimates. The convergence analysis is performed for differential …

[HTML][HTML] Higher-order Haar wavelet method for vibration analysis of nanobeams

J Majak, B Shvartsman, M Ratas, D Bassir… - Materials Today …, 2020 - Elsevier
In this study, the recently developed higher-order Haar wavelet method (HOHWM) was
applied in the vibration analysis of nanobeams. The method was evaluated for different …

Static response and buckling loads of multilayered composite beams using the refined zigzag theory and higher-order Haar wavelet method

M Sorrenti, M Di Sciuva, J Majak… - Mechanics of Composite …, 2021 - Springer
The paper presents a review of Haar wavelet methods and an application of the higher-
order Haar wavelet method to study the behavior of multilayered composite beams under …

Solving nonlinear PDEs using the higher order Haar wavelet method on nonuniform and adaptive grids

M Ratas, A Salupere, J Majak - Mathematical Modelling and …, 2021 - journals.vilniustech.lt
The higher order Haar wavelet method (HOHWM) is used with a nonuniform grid to solve
nonlinear partial differential equations numerically. The Burgers' equation, the Korteweg–de …

A Haar wavelet approximation for two-dimensional time fractional reaction–subdiffusion equation

Ö Oruç, A Esen, F Bulut - Engineering with Computers, 2019 - Springer
In this study, we established a wavelet method, based on Haar wavelets and finite difference
scheme for two-dimensional time fractional reaction–subdiffusion equation. First by a finite …

[HTML][HTML] A high-order reliable and efficient Haar wavelet collocation method for nonlinear problems with two point-integral boundary conditions

M Ahsan, W Lei, AA Khan, A Ullah, S Ahmad… - Alexandria Engineering …, 2023 - Elsevier
The primary goal of this study is to increase and improve the precision and order of
convergence of the well-known Haar wavelet collocation method (HWCM) that is named as …