numerical-mooc/lessons/02_spacetime/README.md

Module 2:

Space & Time: Introduction to numerical solution of PDEs

Summary

This module lays the foundation for numerical solution of partial differential equations (PDEs), where the unknown is a multi-variate function.

• Lesson 1 starts with the simplest model: the one-dimensional linear convection equation, and explains the finite-difference method of discretizing derivatives. It demonstrates the first-order forward-time, backward-space method and discusses truncation error. It then shows how to solve the nonlinear convection equation, and explains vectorized stencil operations.
• Lesson 2 treats stability and the CFL condition, including numerical experimentation and a graphical interpretation using the idea of domain of dependence of the numerical scheme.
• Lesson 3 deals with the one-dimensional diffusion equation, and introduces the discretization of second-order derivatives. It also shows how to create animations within IPython Notebooks.
• Lesson 4 combines previous results to demonstrate a solution of the Burgers' equation. It introduces SymPy for symbolic computations and uses periodic boundary conditions for the first time. It also demonstrates computational speed differences when using array operations.

Badge earning

Completion of this module in the online course platform can earn the learner the Module 2 badge.

Description: What does this badge represent?

The earner of this badge has completed Module 2 of the course "Practical Numerical Methods with Python." This module lays the foundation for the numerical solution of PDEs, including: one-dimensional linear convection, non-linear convection, diffusion and Burgers' equation.

Criteria: What needs to be done to earn it?

To earn this badge, the learner needs to complete the graded assessment in the course platform including: answering quiz about stencils of numerical schemes; answering quiz questions about stability and using sympy; completing the individual coding assignment "Traffic flow" and answering the numeric questions online. Earners should also have completed self-study of the four module lessons, by reading, reflecting on and writing their own version of the codes. This is not directly assessed, but it is assumed. Thus, earners are encouraged to provide evidence of this self-study by giving links to their code repositories or other learning objects they created in the process.

Evidence: Website (link to original digital content)

Desirable: link to the earner's GitHub repository (or equivalent) containing the solution to the "Traffic flow" coding assignment.

Optional: link to the earner's GitHub repository (or equivalent) containing other codes, following the lesson.

Category:

Higher education, graduate

Tags:

engineering, computation, higher education, numericalmooc, python, gwu, george washington university, lorena barba, github

Relevant Links: Is there more information on the web?

Course About page

Course wiki

Course GitHub repo