scholarly journals Numerical Solution of Two-Dimensional Linear Fuzzy Fredholm Integral Equations by the Fuzzy Lagrange Interpolation

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
H. Nouriani ◽  
R. Ezzati
Keyword(s):  
Integral Equation ◽  
Stability Analysis ◽  
Iterative Method ◽  
Fredholm Integral Equation ◽  
Numerical Stability ◽  
Lagrange Interpolation ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
New Approach ◽  
Numerical Stability Analysis

In this study, at first, we propose a new approach based on the two-dimensional fuzzy Lagrange interpolation and iterative method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equation (2DLFFIE). Then, we prove convergence analysis and numerical stability analysis for the proposed numerical algorithm by two theorems. Finally, by some examples, we show the efficiency of the proposed method.

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

scholarly journals A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Meilan Sun ◽  
Chuanqing Gu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Recursive Algorithm ◽  
High Order ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Initial Value ◽  
Numerical Examples ◽  
Type Approximation

The function-valued Padé-type approximation (2DFPTA) is used to solve two-dimensional Fredholm integral equation of the second kind. In order to compute 2DFPTA, a triangle recursive algorithm based on Sylvester identity is proposed. The advantage of this algorithm is that, in the process of calculating 2DFPTA to avoid the calculation of the determinant, it can start from the initial value, from low to high order, and gradually proceeds. Compared with the original two methods, the numerical examples show that the algorithm is effective.

A novel technique based on Bernoulli wavelets for numerical solutions of two-dimensional Fredholm integral equation of second kind

2019 ◽  
Vol 36 (6) ◽  
pp. 1798-1819
Author(s):  
S. Saha Ray ◽  
S. Behera
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Numerical Solutions ◽  
Bernoulli Polynomials ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Content Type ◽  
Good Convergence ◽  
Novel Technique

Purpose A novel technique based on Bernoulli wavelets has been proposed to solve two-dimensional Fredholm integral equation of second kind. Bernoulli wavelets have been created by dilation and translation of Bernoulli polynomials. This paper aims to introduce properties of Bernoulli wavelets and Bernoulli polynomials. Design/methodology/approach To solve the two-dimensional Fredholm integral equation of second kind, the proposed method has been used to transform the integral equation into a system of algebraic equations. Findings Numerical experiments shows that the proposed two-dimensional wavelets technique can give high-accurate solutions and good convergence rate. Originality/value The efficiency of newly developed two-dimensional wavelets technique has been validated by different illustrative numerical examples to solve two-dimensional Fredholm integral equations.

Numerical stability analysis of the Taylor-Couette flow in the two-dimensional case

2009 ◽  
Vol 49 (4) ◽  
pp. 729-742 ◽  
Author(s):  
O. M. Belotserkovskii ◽  
V. V. Denisenko ◽  
A. V. Konyukhov ◽  
A. M. Oparin ◽  
O. V. Troshkin ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Couette Flow ◽  
Numerical Stability ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Numerical Stability Analysis ◽  
Taylor Couette ◽  
Taylor Couette Flow

The Numerical Stability Analysis of Pipelined Conjugate Gradient Methods: Historical Context and Methodology

2018 ◽  
Vol 40 (5) ◽  
pp. A3549-A3580 ◽  
Author(s):  
Erin C. Carson ◽  
Miroslav Rozložník ◽  
Zdeněk Strakoš ◽  
Petr Tichý ◽  
Miroslav Tůma
Keyword(s):  
Stability Analysis ◽  
Conjugate Gradient ◽  
Numerical Stability ◽  
Historical Context ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Numerical Stability Analysis

scholarly journals Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials

2010 ◽  
Vol 2 (2) ◽  
pp. 264-272 ◽  
Author(s):  
A. Shirin ◽  
M. S. Islam
Keyword(s):  
Integral Equation ◽  
Galerkin Method ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Fredholm Integral Equations ◽  
Matrix Formulation ◽  
Piecewise Polynomials ◽  
The Galerkin Method

In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are used as the approximation of basis functions. Examples are considered to verify the effectiveness of the proposed derivations, and the numerical solutions guarantee the desired accuracy.  Keywords: Fredholm integral equation; Galerkin method; Bernstein polynomials. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.4483               J. Sci. Res. 2 (2), 264-272 (2010) 

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