Abstract
This paper is concerned with finite difference solutions of a class of fourth-order nonlinear elliptic boundary value problems. The nonlinear function is not necessarily monotone. A new monotone iterative technique is developed, and three basic monotone iterative processes for the finite difference system are constructed. Several theoretical comparison results among the various monotone sequences are given. A simple and easily verified condition is obtained to guarantee a geometric convergence of the iterations. Numerical results for a model problem with known analytical solution are given.
| Original language | English |
|---|---|
| Pages (from-to) | 1081-1096 |
| Number of pages | 16 |
| Journal | Applied Numerical Mathematics |
| Volume | 57 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 2007 |
Keywords
- Finite difference systems
- Fourth-order elliptic equations
- Monotone iterations
- Rate of convergence
- Upper and lower solutions