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 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 Solving linear two-dimensional Fredholm integral equations system by triangular functions

2016 ◽  
Vol 5 (4) ◽  
pp. 187 ◽  
Author(s):  
Elias Hengamian Asl ◽  
Jafar Nadjafi
Keyword(s):  
Exact Solution ◽  
Linear System ◽  
Numerical Method ◽  
Integral Equations ◽  
Computer Simulations ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
The Given

In this paper, we intend to offer a numerical method to solve linear two-dimensional Fredholm integral equations system of the second kind. This method converts the given two-dimensional Fredholm integral equations system into a linear system of algebraic equations by using twodimensional triangular functions. Moreover, we prove the convergence of the method. Finally the proposed method is illustrated by two examples and also results are compared with the exact solution by using computer simulations.

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