论文标题
关于隐式普通微分方程的数值分析和可视化
On the Numerical Analysis and Visualisation of Implicit Ordinary Differential Equations
论文作者
论文摘要
我们讨论如何将微分方程的几何理论用于隐式普通微分方程的数值集成和可视化，尤其是方程式的奇异性。船只理论会自动将隐式微分方程转换为歧管上的向量场分布，从而将其分析减少到动态系统理论中的标准问题，例如矢量场的整合和不变流形的确定。对于低维情况的可视化，我们将Jobard和Lefer的流线算法适应2.5和3维度。讨论了MATLAB中的具体实现，并提出了一些具体示例。
We discuss how the geometric theory of differential equations can be used for the numerical integration and visualisation of implicit ordinary differential equations, in particular around singularities of the equation. The Vessiot theory automatically transforms an implicit differential equation into a vector field distribution on a manifold and thus reduces its analysis to standard problems in dynamical systems theory like the integration of a vector field and the determination of invariant manifolds. For the visualisation of low-dimensional situations we adapt the streamlines algorithm of Jobard and Lefer to 2.5 and 3 dimensions. A concrete implementation in Matlab is discussed and some concrete examples are presented.
