Abstract
Nonlinear operator equations of the type f(u) ≡ Lu + Nu = 0, u ∈ D(L) are considered, where L is a closed linear operator from a Banach space X to another Banach space Y and N a nonlinear operator from X to Y. A method is presented for numerical verification and inclusion of solutions for the equations. As an example, the existence of a periodic solution is proved for the Duffing equation.
| Original language | English |
|---|---|
| Pages (from-to) | 171-185 |
| Number of pages | 15 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 60 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 1995 Jun 20 |
Keywords
- Computer-assisted existence proof
- Duffing's equation
- Newton's method
- Self-validating numerics
- Urabe-Galerkin's method
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics