Abstract
A parallel monotone iterative relaxation method for a class of two-dimensional discrete boundary value problems is established, and the sequence of iterations is shown to converge monotonically either from above or below to a solution of the problem. This monotone convergence result yields a parallel computational algorithm as well as an existence-comparison result for the solutions. To compute the sequence of iterations, the Thomas algorithm can be used in the same fashion as for one-dimensional problem. The existence and comparison results of the upper and lower solutions are given. The local as well as global existence-uniqueness of the solution are obtained. The global convergence of the iterations is investigated, and the influence of the parameters on the rate of convergence of the iterations is analyzed. Numerical results are given to corroborate the analytical results.
| Original language | English |
|---|---|
| Pages (from-to) | 887-903 |
| Number of pages | 17 |
| Journal | Computers and Mathematics with Applications |
| Volume | 45 |
| Issue number | 6-9 |
| DOIs | |
| State | Published - Mar 2003 |
Keywords
- Convergence rate
- Discrete boundary value problem
- Existence and uniqueness
- Monotone convergence
- Parallel monotone iterative relaxation method
- Upper and lower solution