论文标题
一种基于逻辑的方法，用于寻找隐性普通微分方程的真实奇异性
A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations
论文作者
论文摘要
我们讨论使用逻辑方法上隐性普通微分方程对实数的几何奇异性的有效计算。通过微分方程的容器理论，几何奇异性可以被描述为某些方程式线性系统的行为发生变化。可以使用特定适应的高斯消除参数概括与启发式简化技术和实际量化器消除方法相结合来发现这些点。我们使用原型实现来证明我们的方法与计算实验的相关性和适用性。
We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be characterised as points where the behaviour of a certain linear system of equations changes. These points can be discovered using a specifically adapted parametric generalisation of Gaussian elimination combined with heuristic simplification techniques and real quantifier elimination methods. We demonstrate the relevance and applicability of our approach with computational experiments using a prototypical implementation in Reduce.
