Discrete superconvergent degenerate kernel method for Fredholm integral equations

2019 ◽  
Vol 164 ◽  
pp. 24-32
Author(s):  
C. Allouch ◽  
A. Boujraf ◽  
M. Tahrichi
Keyword(s):  
Integral Equations ◽  
Kernel Method ◽  
Fredholm Integral Equations ◽  
Degenerate Kernel

scholarly journals Algebraic Kernel Method for Solving Fredholm Integral Equations

2016 ◽  
Vol 7 ◽  
pp. 25-33
Author(s):  
Mohammad Shami Hasso
Keyword(s):  
Exact Solution ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Kernel Method ◽  
Algebraic Function ◽  
Taylor Series Expansion ◽  
Fredholm Integral Equations ◽  
Degenerate Kernel ◽  
Fredholm Determinants ◽  
Suggested Technique

In this paper, we study the exact solution of linear Fredholm integral equations using some classical methods including degenerate kernel method and Fredholm determinants method. We propose an analytical method for solving such integral equations. This work has some goals related to suggested technique for solving Fredholm integral equations. The primary goal gives analytical solutions of such equations with minimum steps. Another goal is to compare the suggested method used in this study with classical methods. The final goal is that the propose method is an explicit formula that can be studied in detail for non-algebraic function kernels by using Taylor series expansion and for system of Fredholm integral equations.

scholarly journals A Unified Formulation of Analytical and Numerical Methods for Solving Linear Fredholm Integral Equations

Algorithms ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 293
Author(s):  
Efthimios Providas
Keyword(s):  
Banach Space ◽  
Approximate Solution ◽  
Integral Equations ◽  
Kernel Methods ◽  
Projection Methods ◽  
Analytic Solutions ◽  
Computational Method ◽  
Fredholm Integral Equations ◽  
Degenerate Kernel ◽  
Quadrature Methods

This article is concerned with the construction of approximate analytic solutions to linear Fredholm integral equations of the second kind with general continuous kernels. A unified treatment of some classes of analytical and numerical classical methods, such as the Direct Computational Method (DCM), the Degenerate Kernel Methods (DKM), the Quadrature Methods (QM) and the Projection Methods (PM), is proposed. The problem is formulated as an abstract equation in a Banach space and a solution formula is derived. Then, several approximating schemes are discussed. In all cases, the method yields an explicit, albeit approximate, solution. Several examples are solved to illustrate the performance of the technique.

scholarly journals The Combined Reproducing Kernel Method and Taylor Series for Solving Weakly Singular Fredholm Integral Equations

2016 ◽  
Vol 5 (3) ◽  
pp. 109
Author(s):  
Azizallah Alvandi ◽  
Mahmoud Paripour
Keyword(s):  
Integral Equations ◽  
Taylor Series ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Fredholm Integral Equations ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Reproducing Kernel Method ◽  
Weakly Singular ◽  
Reproducing Kernel Function

<p>In this paper, a numerical method is proposed for solving weakly singular Fredholm integral equations in Hilbert reproducing kernel space (RKHS). The Taylor series is used to remove singularity and reproducing kernel function are used as a basis. The effectiveness and stability of the numerical scheme is illustrated through two numerical examples.</p>

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