Logarithmic reduction of the wrapping effect with application to ordinary differential equations. (English) Zbl 0638.65068
The authors want to bound the wrapping effect for the solutions of a system of linear ordinary differential equations under two-point boundary value conditions. Using known result on the multiplication of interval matrices they show that the usual exponential growth of the wrapping effect can be reduced to polynomial growth by the so called odd/even reduction. - It seems that the authors are unaware of the fact that in their case the wrapping effect can be completely eliminatedö For initial value problems this is, e.g., discussed by the reviewer [ZAMM 66, 513-523 (1986; Zbl 0619.65063)]. This approach can also be used to solve the problem treated here.
Reviewer: K.Nickel
MSC:
65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
65G30 | Interval and finite arithmetic |
34B05 | Linear boundary value problems for ordinary differential equations |