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  • 1
    Electronic Resource
    Electronic Resource
    Optimal growth strategies when mortality and production rates are size-dependent (1993)
    Springer
    Evolutionary ecology 7 (1993), S. 576-592 
    Details
    ISSN: 1573-8477
    Keywords: optimal growth strategy ; optimal energy allocation ; life-history theory ; indeterminate growth
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded ‘bang-bang’ solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01237822
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the numerical integration of a class of singular perturbation problems (1989)
    Springer
    Journal of optimization theory and applications 60 (1989), S. 439-452 
    Details
    ISSN: 1573-2878
    Keywords: Ordinary differential equations ; singular perturbations ; boundary-value problems ; finite-difference approximations ; numerical stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A three-point difference scheme recently proposed in Ref. 1 for the numerical solution of a class of linear, singularly perturbed, two-point boundary-value problems is investigated. The scheme is derived from a first-order approximation to the original problem with a small deviating argument. It is shown here that, in the limit, as the deviating argument tends to zero, the difference scheme converges to a one-sided approximation to the original singularly perturbed equation in conservation form. The limiting scheme is shown to be stable on any uniform grid. Therefore, no advantage arises from using the deviating argument, and the most accurate and efficient results are obtained with the deviation at its zero limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940347
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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