Geodesic
A fixed point method to solve differential equation and Fredholm integral equation
Nyein, Ei Ei 1 ; Zaw, Aung Khaing 2
1 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2 School of Mathematics and Statistics, Beijing Institute of Technology, , Beijing 100081, China
Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 4, p. 205-211.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.013.04.05
Classification : 47H10, 45B05
Keywords: Fixed point method, ODE and PDE, Fredholm integral equation, estimation

Nyein, Ei Ei  1 ; Zaw, Aung Khaing  2

1 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
2 School of Mathematics and Statistics, Beijing Institute of Technology, , Beijing 100081, China 
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Nyein, Ei Ei ; Zaw, Aung Khaing . A fixed point method to solve differential equation and Fredholm integral equation. Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 4, p. 205-211. doi : 10.22436/jnsa.013.04.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.04.05/

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