A note on the Taylor’s decomposition on four points for a third-order differential equation. (English) Zbl 1130.65068
The authors first present Taylor’s decomposition on four points, then construct three-step difference schemes of fourth-order of accuracy for the approximate solutions of an initial-value problem, a boundary-value problem and a nonlocal boundary-value problem for a third-order differential equation, and give some numerical examples.
Reviewer: Ziwen Jiang (Shandong)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
Taylor’s decomposition on four points; third-order differential equation; three-step difference schemes; initial-value problem; boundary-value problem; numerical examplesReferences:
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