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- W3202286773 abstract "Phenomena that change over time are abundant in nature. Dynamical systems, composed of differential equations, are used to model them. In some cases, analytical solutions exist that provide an exact description of the system’s behavior. Otherwise we use numerical approximations: we discretize the original problem over time, where each state of the system at any discrete time moment depends on previous/subsequent states. This process may yield large systems of equations. Efficient tools exist to solve dynamical systems, but might not be well suited for certain types of problems. For example, Runge-Kutta-based solution techniques do not easily handle parameters’ uncertainty, although inherent to real world measurements. If the problem has multiple solutions, such methods usually provide only one. When they cannot find a solution, it is not know whether none exists or it failed to find one. Interval methods, on the other hand, provide guaranteed numerical computations. If a solution exists, it will be found. Interval methods for dynamical systems fall into two main categories: step-based methods (fast but too conservative with overestimation for large systems) and constraint-solving techniques (better at controlling overestimation but usually much slower). In this article, we propose an approach that “slices” large systems into smaller, overlapping ones that are solved using constraint-solving techniques. Our goal is to reduce the computation time and control overestimation, at the expense of solving multiple smaller problems instead of a larger one. We share promising preliminary experimental results." @default.
- W3202286773 created "2021-10-11" @default.
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- W3202286773 date "2021-01-01" @default.
- W3202286773 modified "2023-09-25" @default.
- W3202286773 title "Solving Dynamical Systems Using Windows of Sliding Subproblems" @default.
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- W3202286773 doi "https://doi.org/10.1007/978-3-030-86702-7_2" @default.
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