An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics

2019 ◽  
Vol 525 ◽  
pp. 1440-1448 ◽  
Author(s):  
C.S. Singh ◽  
Harendra Singh ◽  
Somveer Singh ◽  
Devendra Kumar
Keyword(s):  
Integral Equations ◽  
Computational Method ◽  
Abel Integral Equations

scholarly journals Hybrid Rational Haar Wavelet and Block Pulse Functions Method for Solving Population Growth Model and Abel Integral Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
E. Fathizadeh ◽  
R. Ezzati ◽  
K. Maleknejad
Keyword(s):  
Population Growth ◽  
Exact Solutions ◽  
Integral Equations ◽  
Growth Model ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Computational Method ◽  
Block Pulse Functions ◽  
Abel Integral Equations

We use a computational method based on rational Haar wavelet for solving nonlinear fractional integro-differential equations. To this end, we apply the operational matrix of fractional integration for rational Haar wavelet. Also, to show the efficiency of the proposed method, we solve particularly population growth model and Abel integral equations and compare the numerical results with the exact solutions.

scholarly journals A family of methods for Abel integral equations of the second kind

1991 ◽  
Vol 34 (2) ◽  
pp. 211-219 ◽  
Author(s):  
H. Brunner ◽  
M.R. Crisci ◽  
E. Russo ◽  
A. Vecchio
Keyword(s):  
Integral Equations ◽  
Abel Integral Equations

Numerical study of stochastic Volterra–Fredholm integral equations by using second kind Chebyshev wavelets

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Parastoo Adhami
Keyword(s):  
Integral Equations ◽  
Numerical Study ◽  
Operational Matrix ◽  
Computational Method ◽  
Fredholm Integral Equations ◽  
Wavelet Method ◽  
Chebyshev Wavelets ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Efficiency And Reliability

AbstractIn this paper, we present a computational method for solving stochastic Volterra–Fredholm integral equations which is based on the second kind Chebyshev wavelets and their stochastic operational matrix. Convergence and error analysis of the proposed method are investigated. Numerical results are compared with the block pulse functions method for some non-trivial examples. The obtained results reveal efficiency and reliability of the proposed wavelet method.

scholarly journals Convergence of approximate solution of mixed Hammerstein type integral equations

2018 ◽  
Vol 38 (2) ◽  
pp. 61-74
Author(s):  
Monireh Nosrati Sahlan
Keyword(s):  
Galerkin Method ◽  
Integral Equations ◽  
Basis Functions ◽  
Computational Method ◽  
Operational Matrices ◽  
B Spline ◽  
Spline Wavelets ◽  
Type Integral ◽  
The Galerkin Method ◽  
Dual Functions

In the present paper, a computational method for solving nonlinear Volterra-Fredholm Hammerestein integral equations is proposed by using compactly supported semiorthogonal cubic B-spline wavelets as basis functions. Dual functions and Operational matrices of B-spline wavelets via Galerkin method are utilized to reduce the computation of integral equations to some algebraic system, where in the Galerkin method dual of B-spline wavelets are applied as weighting functions. The method is computationally attractive, and applications are demonstrated through illustrative examples.

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