Haar wavelet method for solving integral equations and evolution equations

2008 ◽  
pp. 44-44 ◽  
Author(s):  
Ülo Lepik
Keyword(s):  
Integral Equations ◽  
Evolution Equations ◽  
Haar Wavelet ◽  
Wavelet Method ◽  
Haar Wavelet Method

scholarly journals A Comparative Study on Haar Wavelet and Hosaya Polynomial for the numerical solution of Fredholm integral equations

2018 ◽  
Vol 3 (2) ◽  
pp. 447-458 ◽  
Author(s):  
S.C. Shiralashetti ◽  
H. S. Ramane ◽  
R.A. Mundewadi ◽  
R.B. Jummannaver
Keyword(s):  
Error Analysis ◽  
Comparative Study ◽  
Numerical Solution ◽  
Integral Equations ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Polynomial Method ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Hosoya Polynomial

AbstractIn this paper, a comparative study on Haar wavelet method (HWM) and Hosoya Polynomial method(HPM) for the numerical solution of Fredholm integral equations. Illustrative examples are tested through the error analysis for efficiency. Numerical results are shown in the tables and figures.

scholarly journals APPLICATION OF HIGHER ORDER HAAR WAVELET METHOD FOR SOLVING NONLINEAR EVOLUTION EQUATIONS

2020 ◽  
Vol 25 (2) ◽  
pp. 271-288 ◽  
Author(s):  
Mart Ratas ◽  
Andrus Salupere
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Haar Wavelet ◽  
Higher Order ◽  
Nonlinear Evolution Equations ◽  
Wavelet Method ◽  
Haar Wavelet Method

The recently introduced higher order Haar wavelet method is treated for solving evolution equations. The wave equation, the Burgers’ equations and the Korteweg-de Vries equation are considered as model problems. The detailed analysis of the accuracy of the Haar wavelet method and the higher order Haar wavelet method is performed. The obtained results are validated against the exact solutions.

scholarly journals Haar Wavelet Method for the System of Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Hassan A. Zedan ◽  
Eman Alaidarous
Keyword(s):  
Exact Solution ◽  
Numerical Solution ◽  
Integral Equations ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Test Problems ◽  
Wavelet Method ◽  
System Of Integral Equations ◽  
Haar Wavelet Method ◽  
Comparison Of The Results

We employed the Haar wavelet method to find numerical solution of the system of Fredholm integral equations (SFIEs) and the system of Volterra integral equations (SVIEs). Five test problems, for which the exact solution is known, are considered. Comparison of the results is obtained by the Haar wavelet method with the exact solution.

scholarly journals An operational Haar wavelet method for solving fractional Volterra integral equations

2011 ◽  
Vol 21 (3) ◽  
pp. 535-547 ◽  
Author(s):  
Habibollah Saeedi ◽  
Nasibeh Mollahasani ◽  
Mahmoud Moghadam ◽  
Gennady Chuev
Keyword(s):  
Integral Equations ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Volterra Integral Equations ◽  
Algebraic Equations ◽  
Global Error Bound ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Abel Integral Equations

An operational Haar wavelet method for solving fractional Volterra integral equationsA Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.

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