Application of Triangular and Delta Basis Functions to Solve Linear Fredholm Fuzzy Integral Equation of the Second Kind

2014 ◽  
Vol 39 (5) ◽  
pp. 3969-3978 ◽  
Author(s):  
Farshid Mirzaee ◽  
Mahmoud Paripour ◽  
Mohammad Komak Yari
Keyword(s):  
Integral Equation ◽  
Basis Functions ◽  
Fuzzy Integral

scholarly journals A Highly Efficient and Accurate Finite Iterative Method for Solving Linear Two-Dimensional Fredholm Fuzzy Integral Equations of the Second Kind Using Triangular Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Mohamed A. Ramadan ◽  
Heba S. Osheba ◽  
Adel R. Hadhoud
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Equation System ◽  
Basis Functions ◽  
Computational Method ◽  
Fuzzy Integral ◽  
Two Dimensional ◽  
Orthogonal Functions ◽  
Triangular Form ◽  
Finite Iterative Method

This work introduces a computational method for solving the linear two-dimensional fuzzy Fredholm integral equation of the second form (2D-FFIE-2) based on triangular basis functions. We have used the parametric form of fuzzy functions and transformed a 2D-FFIE-2 with three variables in crisp case to a linear Fredholm integral equation of the second kind. First, a method based on the use of two m-sets of orthogonal functions of triangular form is implemented on the integral equation under study to be changed to coupled algebraic equation system. In order to solve these two schemes, a finite iterative algorithm is then applied to evaluate the coefficients that provided the approximate solution of the integral problems. Three examples are given to clarify the efficiency and accuracy of the method. The obtained numerical results are compared with other direct and exact solutions.

A meshless local Galerkin integral equation method for solving a type of Darboux problems based on the radial basis functions

2021 ◽  
Vol 63 ◽  
pp. 469-492
Author(s):  
Pouria Assari ◽  
Fatemeh Asadi-Mehregan ◽  
Mehdi Dehghan
Keyword(s):  
Integral Equation ◽  
Radial Basis Functions ◽  
Integral Equation Method ◽  
Basis Functions ◽  
Computer Memory ◽  
Shape Functions ◽  
Integration Rule ◽  
Radial Basis ◽  
Small Set ◽  
Discrete Galerkin Method

The main goal of this paper is to solve a class of Darboux problems by converting them into the two-dimensional nonlinear Volterra integral equation of the second kind. The scheme approximates the solution of these integral equations using the discrete Galerkin method together with local radial basis functions, which use a small set of data instead of all points in the solution domain. We also employ the Gauss–Legendre integration rule on the influence domains of shape functions to compute the local integrals appearing in the method. Since the scheme is constructed on a set of scattered points and does not require any background meshes, it is meshless. The error bound and the convergence rate of the presented method are provided. Some illustrative examples are included to show the validity and efficiency of the new technique. Furthermore, the results obtained demonstrate that this method uses much less computer memory than the method established using global radial basis functions. doi:10.1017/S1446181121000377

A MESHLESS LOCAL GALERKIN INTEGRAL EQUATION METHOD FOR SOLVING A TYPE OF DARBOUX PROBLEMS BASED ON RADIAL BASIS FUNCTIONS

2021 ◽  
pp. 1-24
Author(s):  
P. ASSARI ◽  
F. ASADI-MEHREGAN ◽  
M. DEHGHAN
Keyword(s):  
Integral Equation ◽  
Radial Basis Functions ◽  
Integral Equation Method ◽  
Basis Functions ◽  
Computer Memory ◽  
Shape Functions ◽  
Integration Rule ◽  
Radial Basis ◽  
Small Set ◽  
Discrete Galerkin Method

Abstract The main goal of this paper is to solve a class of Darboux problems by converting them into the two-dimensional nonlinear Volterra integral equation of the second kind. The scheme approximates the solution of these integral equations using the discrete Galerkin method together with local radial basis functions, which use a small set of data instead of all points in the solution domain. We also employ the Gauss–Legendre integration rule on the influence domains of shape functions to compute the local integrals appearing in the method. Since the scheme is constructed on a set of scattered points and does not require any background meshes, it is meshless. The error bound and the convergence rate of the presented method are provided. Some illustrative examples are included to show the validity and efficiency of the new technique. Furthermore, the results obtained demonstrate that this method uses much less computer memory than the method established using global radial basis functions.

On the basic solutions to the generalized fuzzy integral equation

1998 ◽  
Vol 95 (2) ◽  
pp. 255-260 ◽  
Author(s):  
Wu Congxin ◽  
Song Shiji ◽  
Wang Haiyan
Keyword(s):  
Integral Equation ◽  
Fuzzy Integral ◽  
Basic Solutions
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