scholarly journals Fast multiscale Galerkin methods for solving ill-posed integral equations via a coupled system under general source conditions

2013 ◽  
Vol 408 (1) ◽  
pp. 213-224 ◽  
Author(s):  
Shengpei Ding ◽  
Hongqi Yang
Keyword(s):  
Integral Equations ◽  
Coupled System ◽  
Galerkin Methods ◽  
Ill Posed ◽  
General Source

Multiscale collocation methods for ill-posed integral equations via a coupled system

2012 ◽  
Vol 28 (2) ◽  
pp. 025006 ◽  
Author(s):  
Zhongying Chen ◽  
Shengpei Ding ◽  
Yuesheng Xu ◽  
Hongqi Yang
Keyword(s):  
Integral Equations ◽  
Coupled System ◽  
Collocation Methods ◽  
Ill Posed

scholarly journals Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Monnanda Erappa Shobha ◽  
Santhosh George
Keyword(s):  
Integral Equation ◽  
Iterative Method ◽  
Iterative Scheme ◽  
Initial Guess ◽  
Optimal Order ◽  
Source Condition ◽  
Adaptive Scheme ◽  
Actual Solution ◽  
Ill Posed ◽  
General Source

Recently, Vasin and George (2013) considered an iterative scheme for approximately solving an ill-posed operator equationF(x)=y. In order to improve the error estimate available by Vasin and George (2013), in the present paper we extend the iterative method considered by Vasin and George (2013), in the setting of Hilbert scales. The error estimates obtained under a general source condition onx0-x^(x0is the initial guess andx^is the actual solution), using the adaptive scheme proposed by Pereverzev and Schock (2005), are of optimal order. The algorithm is applied to numerical solution of an integral equation in Numerical Example section.

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.

Sign in / Sign up

Export Citation Format

Share Document