Convergence analysis of a highly accurate Nyström scheme for Fredholm integral equations

2020 ◽  
Vol 152 ◽  
pp. 231-242
Author(s):  
Fadi Awawdeh ◽  
Linda Smail
Keyword(s):  
Convergence Analysis ◽  
Integral Equations ◽  
Fredholm Integral Equations

scholarly journals A Novel and Efficient Numerical Algorithm for Solving 2D Fredholm Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
H. Bin Jebreen
Keyword(s):  
Approximate Solution ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Numerical Algorithm ◽  
Numerical Experiments ◽  
Operational Matrix ◽  
Fredholm Integral Equations ◽  
Scaling Functions ◽  
Algebraic Equations

A novel and efficient numerical method is developed based on interpolating scaling functions to solve 2D Fredholm integral equations (FIE). Using the operational matrix of integral for interpolating scaling functions, FIE reduces to a set of algebraic equations that one can obtain an approximate solution by solving this system. The convergence analysis is investigated, and some numerical experiments confirm the accuracy and validity of the method. To show the ability of the proposed method, we compare it with others.

scholarly journals Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations

2020 ◽  
pp. 409-415
Author(s):  
Pakhshan Mohammed Ameen Hasan ◽  
Nejmaddin Abdulla Sulaiman
Keyword(s):  
Integral Equation ◽  
Perturbation Method ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Error Estimation ◽  
Homotopy Perturbation Method ◽  
Fredholm Integral Equations ◽  
Homotopy Perturbation ◽  
The Absolute ◽  
Aitken Method

In this paper, the homotopy perturbation method is presented for solving the second kind linear mixed Volterra-Fredholm integral equations. Then, Aitken method is used to accelerate the convergence. In this method, a series will be constructed whose sum is the solution of the considered integral equation. Convergence of the constructed series is discussed, and its proof is given; the error estimation is also obtained. For more illustration, the method is applied on several examples and programs, which are written in MATLAB (R2015a) to compute the results. The absolute errors are computed to clarify the efficiency of the method.

scholarly journals Convergence Analysis for the Homotopy Perturbation Method for a Linear System of Mixed Volterra-Fredholm Integral Equations

2020 ◽  
Vol 17 (3(Suppl.)) ◽  
pp. 1010
Author(s):  
Pakhshan M. Hasan ◽  
Nejmaddin Abdulla Sulaiman
Keyword(s):  
Exact Solution ◽  
Linear System ◽  
Perturbation Method ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Error Estimation ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Fredholm Integral Equations ◽  
Homotopy Perturbation

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

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