scholarly journals AN EFFICIENT NUMERICAL METHOD FOR SOLVING FREDHOLM INTEGRAL EQUATIONS OVER (0,+infty)

2013 ◽  
Vol 85 (2) ◽  
Author(s):  
M.T. Darvishi ◽  
A. Omidi ◽  
F. Khani
Keyword(s):  
Numerical Method ◽  
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.

Application of Bernoulli wavelet method to solve a system of fuzzy integral equations

2018 ◽  
Vol 9 (1-2) ◽  
pp. 16-27 ◽  
Author(s):  
Mohamed Abdel- Latif Ramadan ◽  
Mohamed R. Ali
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Bernoulli Polynomials ◽  
Approximate Solutions ◽  
Fredholm Integral Equations ◽  
Fuzzy Integral ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Numerical Examples ◽  
Bernoulli Wavelet

In this paper, an efficient numerical method to solve a system of linear fuzzy Fredholm integral equations of the second kind based on Bernoulli wavelet method (BWM) is proposed. Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The aim of this paper is to apply Bernoulli wavelet method to obtain approximate solutions of a system of linear Fredholm fuzzy integral equations. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, then we used it to transform the integral equations to the system of algebraic equations. The error estimates of the proposed method is given and compared by solving some numerical examples.

scholarly journals A new numerical method for a class of Volterra and Fredholm integral equations

2020 ◽  
Vol 379 ◽  
pp. 112944
Author(s):  
Paolo De Angelis ◽  
Roberto De Marchis ◽  
Antonio Luciano Martire
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Fredholm Integral Equations

scholarly journals Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
S. Mashayekhi ◽  
M. Razzaghi ◽  
O. Tripak
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Bernoulli Polynomials ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

scholarly journals A Novel Numerical Method of Two-Dimensional Fredholm Integral Equations of the Second Kind

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yanying Ma ◽  
Jin Huang ◽  
Hu Li
Keyword(s):  
Approximate Solution ◽  
Integral Operator ◽  
Numerical Method ◽  
Integral Equations ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Error Analyses ◽  
Approximate Integral

A novel numerical method is developed for solving two-dimensional linear Fredholm integral equations of the second kind by integral mean value theorem. In the proposed algorithm, each element of the generated discrete matrix is not required to calculate integrals, and the approximate integral operator is convergent according to collectively compact theory. Convergence and error analyses of the approximate solution are provided. In addition, an algorithm is given. The reliability and efficiency of the proposed method will be illustrated by comparison with some numerical results.

scholarly journals An Appropriate Numerical Method for Solving Nonlinear Volterra-Fredholm Integral Equations

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Roghayeh Katani 1
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Integral Equations ◽  
Nonlinear Equations ◽  
Fredholm Integral Equations ◽  
Block Method ◽  
Starting Values ◽  
Linear And Nonlinear

This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of some significative examples.

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