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Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this article, conditions under which solutions of some systems of differential equations are bounded are established and their asymptotic properties are studied under the assumption that the solutions of each system are known.
Abstract: We establish conditions under which solutions of some systems of differential equations are bounded and study their asymptotic properties.
1 citations
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01 Jan 19841 citations
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TL;DR: In this article, a continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories, which allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbations until the optimal full-order solution is obtained.
Abstract: A continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories. This method allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbation parameter until the optimal full-order solution is obtained. The method does not require the calculation of higher order correction terms nor does it require the perturbation parameter to be small - thus, it has potentially superior convergence properties compared to conventional asymptotic expansions when the perturbation parameter is large. A simple trajectory optimization problem is considered to illustrate the method.
1 citations