Abstract
A compact finite difference method is proposed for a general class of 2 nth-order Lidstone boundary value problems. The existence and uniqueness of the finite difference solution is investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. A monotone iteration process is provided for solving the resulting discrete system efficiently, and a simple and easily verified condition is obtained to guarantee a geometric convergence of the iterations. The convergence of the finite difference solution and the fourth-order accuracy of the proposed method are proved. Numerical results demonstrate the high efficiency and advantages of this new approach.
| Original language | English |
|---|---|
| Pages (from-to) | 499-521 |
| Number of pages | 23 |
| Journal | Computers and Mathematics with Applications |
| Volume | 56 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jul 2008 |
Keywords
- 2 nth-order Lidstone boundary value problem
- Compact finite difference method
- Fourth-order accuracy
- Monotone iterations
- Rate of convergence