On error bounds forG-stable methods |
| |
Authors: | Olavi Nevanlinna |
| |
Institution: | 1. Institute of Mathematics, Helsinki University of Technology, SF-02150, Espoo 15, Finland
|
| |
Abstract: | Error bounds for numerical solutions of the initial value problem $$y' = f(y), y(0) = \bar y \in R^d ,$$ are derived. The methods (?,σ) are assumed to beG-stable 2], andf satisfies for someμ teR and for some inner product 〈, 〉 the relation $$\left\langle {u - v,f(u)} \right\rangle \leqq \mu \left\| {u - v} \right\|^2 ,u,v \in R^d $$ As corollaries of the bounds we get, forμ=0, the result that whenever the local errors {q n } ∈l 1 then the global errors {z n } ∈l ∞. Forμ<0, assuming in addition that the zeros ofσ(ζ) lie inside the unit circle, {q n } tel p implies {z n } tel p forp ≧ 2. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|