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tandfonline.com – Some prospective criteria for non-unique solutions of ordinary differential equations

tandfonline.com har udgivet en rapport under søgningen “Teacher Education Mathematics”:

ABSTRACT

Ordinary differential equations (ODEs) have a wide range of potential applications in science and engineering with regard to nonlinear dynamic systems. Frequently, there is a focus upon locating unique solutions to ODEs, with non-unique solutions being viewed as potentially problematic. However, some have recognized the importance of examining the character of non-unique solutions as well in order to properly understand the behaviour of physical systems. In some areas of engineering, notably control theory, the latter concern has become pressing. In this paper, by studying the asymptotic stability of second-order ordinary differential systems, we present a theorem creatively and prove it strictly by two lemmas. Using the criteria for non-unique solutions of first-order ordinary differential equations at points of equilibrium, we can solve engineering problems effectively. The applicability of this novel approach to the solution of engineering problems is provided through an example relating to the optimization of finite time controllers.

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Troels Gannerup Christensen

Jeg er ansat som adjunkt hos Læreruddannelsen i Jelling, hvor jeg underviser i matematik, specialiseringsmodulet teknologiforståelse, praktik m.m. Jeg har tidligere været ansat som pædagogisk konsulent i matematik og tysk hos UCL ved Center for Undervisningsmidler (CFU) i Vejle og lærer i udskolingen (7.-9. klasse) på Lyshøjskolen i Kolding. Jeg er ejer af og driver bl.a. hjemmesiderne www.lærklokken.dk og www.iundervisning.dk, ggbkursus.dk og er tidligere fagredaktør på matematik på emu.dk. Jeg går ind for, at læring skal være let tilgængelig og i størst mulig omfang gratis at benytte.

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