In this article, we describe on a state of the art of validated numerical computations for solutions of differential equations. A brief overview of the main techniques for self-validating numerics for initial and boundary value problems in ordinary and partial differential equations including eigenvalue problems will be presented. A fairly detailed introductions are given for the author's own method related to second-order elliptic boundary for the author's own method related to second-order elliptic boundary value problems. Many references which seem to be useful for readers are supplied at the end of the article.
- Computer assisted proof in analysis
- Nonlinear differential equation
- Numerical verification
ASJC Scopus subject areas
- Signal Processing
- Computer Science Applications
- Control and Optimization