Solving Ordinary Differential Equations
Solving Ordinary Differential Equations
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DOI：
10.1007/978-3-319-32428-9_4
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发表时间：
2019-10
期刊：
影响因子：
--
通讯作者：
S. Linge;H. Langtangen
中科院分区：
文献类型：
--
作者：
S. Linge;H. Langtangen
微分方程是理解和预测自然界、工程和社会中动力系统行为的最有力的数学工具之一。动态系统是具有某种状态的系统，通常由一组变量表示，随时间演化。例如，摆动的钟摆、疾病的传播和天气都是动力系统的例子。我们可以用物理学的基本定律或简单的直觉来表达控制系统随时间演化的数学规则。这些规则采用微分方程的形式。
Differential equations constitute one of the most powerful mathematical tools to understand and predict the behavior of dynamical systems in nature, engineering, and society. A dynamical system is some system with some state, usually expressed by a set of variables, that evolves in time. For example, an oscillating pendulum, the spreading of a disease, and the weather are examples of dynamical systems. We can use basic laws of physics, or plain intuition, to express mathematical rules that govern the evolution of a system in time. These rules take the form ofdifferential equations.