In this tutorial, We will answer what’s the usage of ODE? How to solve ODE in Python?
What’s the usage of ODE? How to solve ODE in Python?
Ordinary Differential Equation (ODE) can be used to describe a dynamic system. To some extent, we are living in a dynamic system, the weather outside of the window changes from dawn to dusk, the metabolism occurs in our body is also a dynamic system because thousands of reactions and molecules got synthesized and degraded as time goes.
More formally, if we define a set of variables, like the temperatures in a day, or the amount of molecule X in a certain time point, and it changes with the independent variable *(in a dynamic system, usually it will be *time t). ODE offers us a way to mathematically depict the dynamic changes of defined variables. The opposite system to that is called static system, thinking about taking a photo of the outside, this snapshot doesn’t contain any dynamics, in another word, it is static.
Solving Ordinary Differential Equations means determining how the variables will change as time goes by, the solution, sometimes referred to as solution curve (visually shown as below), provide informative prediction to the default behavior of any dynamic systems.
An example solution curve for a linear system
In this article, I am going to give an introduction to ODE and more important, how to solve ODE merely using Python.
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