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 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.

Application of Haar Wavelet Method for Solving the Nonlinear Fuzzy Integro-Differential Equations

2019 ◽  
Vol 16 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Mohamed R. Ali ◽  
Adel R. Hadhoud
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Haar Wavelet ◽  
Test Problems ◽  
Newton Methods ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Homotopy Perturbation ◽  
Proposed Model

Haar wavelet method (HWM) is an essential profitable method for settling the nonlinear Fuzzy Fredholm integro-differential equations (NFIDE). The proposed model converts the NFIDE into to nonlinear equations which tackle by the familiar Newton methods. The authors investigate the convergence of this method. Test problems are solved to show the accuracy of our method where the obtained numerical results are compared with Homotopy perturbation method (HPM) and the exact solutions. Graphical portrayals of the correct and obtained estimated arrangements illuminate the exactness of the methodology.

Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

2017 ◽  
Vol 18 ◽  
pp. 50-59 ◽  
Author(s):  
S.C. Shiralashetti ◽  
R.A. Mundewadi
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Wavelet Collocation Method

In this paper, we present a numerical solution of nonlinear Volterra-Fredholm integral equations using Haar wavelet collocation method. Properties of Haar wavelet and its operational matrices are utilized to convert the integral equation into a system of algebraic equations, solving these equations using MATLAB to compute the Haar coefficients. The numerical results are compared with exact and existing method through error analysis, which shows the efficiency of the technique.

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