ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991): 65L05 65L06, 65L10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. The solution $y(x,x_0,y_0)$ of an initial-value problem (IVP) $y'(x)=f(x,y)$ , $y(x_0)=y_0$ at a point $x$ is a differentiable function of the initial value $y_0$ provided $\partial f/\partial y$ is continuous. The derivative $\partial y(x,x_0,y_0)/\partial y_0$ of $y$ , which reflects the sensitivity of the IVP, is most frequently computed by a finite difference approximation. In connection with shooting techniques, this sensitivity analysis is the dominant part of the overall computation time and it can be accelerated if sophisticated methods are used. Several different strategies are possible and all lead to very different algorithms. Some of the most promising ones were implemented and compared. It turns out that the computation time can be reduced to less than one fourth compared with a finite difference approximation of $\partial y(x,x_0,y_0)/\partial y_0$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050021
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