Multistep methods on manifolds (Q2713135)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Multistep methods on manifolds |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multistep methods on manifolds |
scientific article |
Statements
Multistep methods on manifolds (English)
0 references
29 November 2001
0 references
differential equation on manifold
0 references
differential algebraic equation
0 references
multistep method
0 references
Taylor method
0 references
preservation of invariants
0 references
error analysis
0 references
Runge-Kutta scheme
0 references
Bateman equation
0 references
The author discusses the preservation of invariants of an ordinary differential equation in a numerical integration. He considers methods of Taylor type, i.e. methods of order \(p\) where the leading term in the error analysis is given by the \((p+1)\)th derivative of the solution. Many classical numerical schemes are of this type, in particular multistep methods; a notable exception are Runge-Kutta schemes. It is first shown that an invariant can be preserved by a method of Taylor type only, if it satisfies the Bateman equation, then that this implies that the invariant must be linear.
0 references
