Скачать с ютуб [Numerical Modeling 12] Finite difference method for (nonlinear) ordinary differential equations в хорошем качестве

[Numerical Modeling 12] Finite difference method for (nonlinear) ordinary differential equations

Let’s start to do more scientific stuff. From now on, we will go for exploring the details of the world of numerical methods, to know how they work and how we can use them to solve complex problems. In this video, we go for a simple introduction to the finite difference method, a very powerful and widely used technique to solve differential equations, and we use it to solve an ordinary differential equation (ODE) model of the phugoid motion. Educational Materials: In order to follow the videos, you need the educational materials, which are provided as a set of Jupyter Notebooks. You can find the materials at http://tuxriders.com/videos/numerical... and https://github.com/TuxRiders/numerica... Topics covered: 🎯 Building the mathematical model of the phugoid motion 🎯 Simplifying nonlinear problems into a linear system 🎯 Understanding the numerical magic behind Euler’s method 🎯 Implementing Euler’s method for initial value problems 🎯 Checking the errors and understanding convergence studies 🎯 The benefits of using higher-order methods rather than first-order Euler Lecturer: Mojtaba Barzegari https://mbarzegary.github.io/ To learn more about the goals of the TuxRiders project, please visit our website at http://tuxriders.com. As stated in the video, original notebooks are taken from the Numerical MOOC (https://github.com/numerical-mooc/num...) Chapters in this video! ################ 0:00 - Intro 00:45 - Introducing the problem, the mathematical model 04:13 - Rewriting the nonlinear model into a linear system 07:29 - Understanding the numerical scheme 13:08 - Solving the initial value problem using the Euler’s method 19:41 - Checking the error and the convergence 21:54 - Solving a more complex model 23:10 - Grid convergence 25:10 - Higher order methods and their benefit