Asymptotic expansion and geometric properties of the spline collocation periodic solution of an ODE system. (English) Zbl 0728.65075
The author studies the asymptotic expansion of the cubic spline collocation periodic solution of an autonomous ordinary differential equation. Some criteria and techniques are developed to prove geometric properties of numerical solutions such as convexity invariance and one side-approximation.
Reviewer: K.Najzar (Praha)
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
asymptotic expansion; cubic spline collocation periodic solution; autonomous ordinary differential equation; geometric properties; convexity invariance; one side-approximationReferences:
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