Coupled System of Nonlinear Fuzzy Volterra–Urysohn Integral Equations

2020 ◽  
pp. 21-35
Author(s):  
Abdelati El Allaoui ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Integral Equations ◽  
Coupled System ◽  
Urysohn Integral Equations

The Sound Transmission Through a Baffled, Thin, Finite, Elastic Plate by Using Boundary Integral Equations

1999 ◽  
Author(s):  
Yasuhito Kawai
Keyword(s):  
Integral Equations ◽  
Elastic Plate ◽  
Boundary Integral Equations ◽  
Sound Transmission ◽  
Coupled System ◽  
Boundary Integral ◽  
Image Method ◽  
Thin Elastic Plate ◽  
Control Engineering ◽  
Sound Fields

Abstract The prediction of sound transmission through a thin elastic plate such as a window is an important problem in the field of noise control engineering. Integral equations which express sound fields in infinite half spaces which are divided off by the baffle and the elastic plate are introduced and combined with the equation of plate vibration to solve as a coupled system. The image method is used in every equation to reduce unknown functions and boundaries which should be considered. Some numerical examples are solved numerically to examine the method.

scholarly journals Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Randhir Singh ◽  
Gnaneshwar Nelakanti ◽  
Jitendra Kumar
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Integral Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Recursive Scheme ◽  
Urysohn Integral Equations ◽  
Adomian Decomposition

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

scholarly journals FIXED POINT RESULTS IN COMPLEX VALUED METRIC SPACES WITH AN APPLICATION

2021 ◽  
pp. 237
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
Liliana Guran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Unique Solution ◽  
Integral Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Urysohn Integral Equations ◽  
Complex Valued

In this paper, we introduce fixed point theorem for a general contractive condition in complex valued metric spaces. Also, some important corollaries under this contractive condition areobtained. As an application, we find a unique solution for Urysohn integral equations and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. [2] and some other known results in the literature.

scholarly journals An Integral Equation Formalism for Integrating a Nonlinear Initial-Boundary Value Problem for a Boussinesq Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
T. S. Jang
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Boussinesq Equation ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Coupled System ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Successive Approximations ◽  
Initial Boundary Value

In this paper, a new nonlinear initial-boundary value problem for a Boussinesq equation is formulated. And a coupled system of nonlinear integral equations, equivalent to the new initial-boundary value problem, is constructed for integrating the initial-boundary value problem, but which is inherently different from other conventional formulations for integral equations. For the numerical solutions, successive approximations are applied, which leads to a functional iterative formula. A propagating solitary wave is simulated via iterating the formula, which is in good agreement with the known exact solution.

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