Wavelet Approximation of Functions Belonging to Generalized Lipschitz Class by Extended Haar Wavelet Series and its Application in the Solution of Bessel Differential Equation Using Haar Operational Matrix

2019 ◽  
Vol 5 (3) ◽  
Author(s):  
Shyam Lal ◽  
Priya Kumari
Keyword(s):  
Differential Equation ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Lipschitz Class ◽  
Approximation Of Functions ◽  
Wavelet Approximation ◽  
Bessel Differential Equation ◽  
Generalized Lipschitz Class ◽  
Wavelet Series

scholarly journals Trigonometric approximation of functions $f(x,y)$ of generalized Lipschitz class by double Hausdorff matrix summability method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abhishek Mishra ◽  
Vishnu Narayan Mishra ◽  
M. Mursaleen
Keyword(s):  
Double Fourier Series ◽  
Degree Of Approximation ◽  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Gamma Delta ◽  
Approximation Of Functions ◽  
Matrix Summability ◽  
Alpha Beta ◽  
Generalized Lipschitz Class ◽  
Hausdorff Matrix

AbstractIn this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$ f ( x , y ) belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$ L i p ( ( ξ 1 , ξ 2 ) ; r ) , $r \geq 1$ r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$ L i p ( ( α , β ) ; r ) and $Lip(\alpha ,\beta )$ L i p ( α , β ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$ ( C , γ , δ ) means.

scholarly journals Legendre wavelet approximation of functions having derivatives of Lipschitz class

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 381-397
Author(s):  
Shyam Lal ◽  
Neha Patel
Keyword(s):  
Wavelet Analysis ◽  
Lipschitz Class ◽  
Second Derivative ◽  
Approximation Of Functions ◽  
Wavelet Approximation ◽  
First Derivative ◽  
Derivatives Of ◽  
Wavelet Estimators

In this paper, Legendre Wavelet approximation of functions f having first derivative f' and second derivative f'' of Lip? class, 0 < ? ? 1, have been determined. These wavelet estimators are sharper, better and best possible in Wavelet Analysis. It is observed that the LegendreWavelet estimator of f whose f'' ? Lip? is sharper than the estimator of f having f ' ?Lip? class.

Haar wavelet operational matrix method for system of fractional nonlinear differential equations

2017 ◽  
Vol 15 (05) ◽  
pp. 1750043 ◽  
Author(s):  
Umer Saeed
Keyword(s):  
Differential Equations ◽  
Reliable Method ◽  
Nonlinear Differential Equations ◽  
Operational Matrix ◽  
Implementation Process ◽  
Haar Wavelet ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Operational Matrix Method ◽  
Fractional Differential

In this paper, we present a reliable method for solving system of fractional nonlinear differential equations. The proposed technique utilizes the Haar wavelets in conjunction with a quasilinearization technique. The operational matrices are derived and used to reduce each equation in a system of fractional differential equations to a system of algebraic equations. Convergence analysis and implementation process for the proposed technique are presented. Numerical examples are provided to illustrate the applicability and accuracy of the technique.

Sign in / Sign up

Export Citation Format

Share Document