scholarly journals New error estimation based on midpoint iterative method for solving nonlinear fuzzy fredholm integral equations

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1773-1782 ◽  
Author(s):  
Vahid Mahaleh ◽  
Reza Ezzati
Keyword(s):  
Iterative Method ◽  
Integral Equations ◽  
Error Estimation ◽  
Quadrature Formula ◽  
Numerical Stability ◽  
Suggested Method ◽  
Successive Approximations ◽  
Fredholm Integral Equations ◽  
Numerical Examples

In this paper, first, we apply the successive approximations method in terms of midpoint quadrature formula to solve nonlinear fuzzy Fredholm integral equations of the second kind (NFFIE-2). Considering some assumptions, we acquire a new error estimation. Moreover, we prove the convergence of the proposed method. Then, we study the numerical stability of the proposed method with respect to the first iteration choice. Eventually, to demonstrate the accuracy of the suggested method, we present two numerical examples.

scholarly journals Numerical solution of two dimensional nonlinear fuzzy Fredholm integral equations of second kind using hybrid of block-pulse functions and Bernstein polynomials

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4923-4935 ◽  
Author(s):  
Vahid Mahaleh ◽  
Reza Ezzati
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Approximation Method ◽  
Numerical Stability ◽  
Bernstein Polynomials ◽  
Fredholm Integral Equations ◽  
Successive Approximation Method ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Block Pulse Functions

In this paper, first, we introduce a successive approximation method in terms of a combination of Bernstein polynomials and block-pulse functions. The proposed method is given for solving two dimensional nonlinear fuzzy Fredholm integral equations of the second kind. Then, we present the convergence of the proposed method. Also we investigate the numerical stability of the method with respect to the choice of the first iteration. Finally, two numerical examples are presented to show the accuracy of the method.

Stress Intensity Factors of Multiple Cracked Sheet With Riveted Stiffeners

1991 ◽  
Vol 113 (3) ◽  
pp. 280-284 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Intensity Factors ◽  
Single Crack ◽  
Numerical Examples ◽  
Unknown Density

A new method is proposed for analyzing the stress intensity factors of multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown density of surface tractions and fastener forces, Fredholm integral equations and compatibility equations of displacements among the sheet, fasteners, and stiffeners are formulated. After solving the unknown density, the stress intensity factors of multiple cracks in the sheet are determined. Some numerical examples are analyzed.

scholarly journals Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid of Block-Pulse Functions and Chebyshev Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Changqing Yang
Keyword(s):  
Integral Equations ◽  
Chebyshev Polynomials ◽  
Mathematical Physics ◽  
Fredholm Integral Equations ◽  
Chebyshev Series ◽  
Fredholm Type ◽  
Numerical Examples ◽  
Block Pulse Functions ◽  
Hybrid Function ◽  
Nonlinear Fredholm Integral Equations

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm-type equations, which have many applications in mathematical physics, are then considered. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Chebyshev series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

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.

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