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
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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.
Share and Cite
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
Keywords
- Fixed point method
- ODE and PDE
- Fredholm integral equation
- estimation
MSC
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