1. Approximation methods for solving the Cauchy problem
- Creator:
- Mortici, Cristinel
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Cauchy problem, Lipschitz function, Picard theorem, succesive approximations method, and contractions principle
- Language:
- English
- Description:
- In this paper we give some new results concerning solvability of the 1-dimensional differential equation $y^{\prime } = f(x,y)$ with initial conditions. We study the basic theorem due to Picard. First we prove that the existence and uniqueness result remains true if $f$ is a Lipschitz function with respect to the first argument. In the second part we give a contractive method for the proof of Picard theorem. These considerations allow us to develop two new methods for finding an approximation sequence for the solution. Finally, some applications are given.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public