Least square approximation of a nonlinear ordinary differential equation. (English) Zbl 0855.65066
The subject of the paper is an optimal linearization method for nonlinear ordinary differential equations. Results concerning an earlier proposed approximation are presented. The main results stipulate that the proposed approximation is of order two with respect to the initial value, and is generally of the same order as the nonlinearity. Necessary and sufficient conditions are given for uniqueness of the elements of the sequence determined in the course of the optimal approximation.
Several examples are included showing satisfactory adequacy of approximate results compared to the exact ones.
Several examples are included showing satisfactory adequacy of approximate results compared to the exact ones.
Reviewer: D.Petcu (Timişoara)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
Keywords:
numerical examples; mean square convergence; stability; linearization method; nonlinear ordinary differential equationsReferences:
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