A computational approach for solving fractional Volterra integral equations based on two dimensional Haar wavelet method

2021 ◽  
pp. 1-20
Author(s):  
Zohreh Abdollahi ◽  
M. MohseniMoghadam ◽  
H. Saeedi ◽  
M. J. Ebadi
Keyword(s):  
Integral Equations ◽  
Haar Wavelet ◽  
Computational Approach ◽  
Volterra Integral Equations ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Haar Wavelet Method

Solving Two-Dimensional Nonlinear Volterra Integral Equations Using Rationalized Haar Functions in the Complex Plane

2020 ◽  
Vol 12 (3) ◽  
pp. 409-415
Author(s):  
Majid Erfanian ◽  
Hamed Zeidabadi ◽  
Rohollah Mehri
Keyword(s):  
Integral Equations ◽  
Order Of Convergence ◽  
Computational Algorithm ◽  
Numerical Solutions ◽  
Haar Wavelet ◽  
Volterra Integral Equations ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Haar Functions ◽  
Banach Theorem

In this work, two-dimensional rational Haar wavelet method has been used to solve the twodimensional Volterra integral equations. By using fixed point Banach theorem we achieved the order of convergence and the rate of convergence is O(n(2q)n). Numerical solutions of three examples are presented by applying a simple and efficient computational algorithm.

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.

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 New Numerical Treatment for a Family of Two-Dimensional Fractional Fredholm Integro-Differential Equations

Algorithms ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 37
Author(s):  
Amer Darweesh ◽  
Marwan Alquran ◽  
Khawla Aghzawi
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Haar Wavelet ◽  
Two Dimensional ◽  
Numerical Treatment ◽  
Wavelet Method ◽  
New Approach ◽  
Robust Algorithm ◽  
Haar Wavelet Method ◽  
The Laplace Transform

In this paper, we present a robust algorithm to solve numerically a family of two-dimensional fractional integro differential equations. The Haar wavelet method is upgraded to include in its construction the Laplace transform step. This modification has proven to reduce the accumulative errors that will be obtained in case of using the regular Haar wavelet technique. Different examples are discussed to serve two goals, the methodology and the accuracy of our new approach.

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.

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