A fixed point method to solve differential equation and Fredholm integral equation

Volume 13, Issue 4, pp 205--211 http://dx.doi.org/10.22436/jnsa.013.04.05
Publication Date: February 28, 2020 Submission Date: November 09, 2019 Revision Date: January 06, 2020 Accteptance Date: January 28, 2020

Authors

Ei Ei Nyein - School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China. Aung Khaing Zaw - School of Mathematics and Statistics, Beijing Institute of Technology, , Beijing 100081, China.


Abstract

The purpose of this research is to explore a fixed point method to solve a class of functional equations, \(Tu=f\), where \(T\) is a differential or an integral operator on a Sobolev space \(H^2(\Omega)\), where \(\Omega\) is an open set in \(\mathbb{R}^n\). First, \(T\) is converted into a sum of \(I+\lambda A\) with \(\lambda>0\), where \(A\) is a continuous linear operator and \(I\) is identity mapping. Then it is shown that \(T\) is a contraction on the prescribed Sobolev space and norm of \(A\) is estimated on the prescribed Sobolev space. By means of the theory of inverse operator of \(I+\lambda A\) and by choosing the appropriate value of \(\lambda\), the solution \(u\) of differential or integral operator is obtained. Some practical problems concerning the linear differential equation and Fredholm integral equation are solved by virtue of the fixed point method.


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ISRP Style

Ei Ei Nyein, Aung Khaing Zaw, A fixed point method to solve differential equation and Fredholm integral equation, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 4, 205--211

AMA Style

Nyein Ei Ei, Zaw Aung Khaing, A fixed point method to solve differential equation and Fredholm integral equation. J. Nonlinear Sci. Appl. (2020); 13(4):205--211

Chicago/Turabian Style

Nyein, Ei Ei, Zaw, Aung Khaing. "A fixed point method to solve differential equation and Fredholm integral equation." Journal of Nonlinear Sciences and Applications, 13, no. 4 (2020): 205--211


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