Over five weeks in the semester, students will work their way through using Matlab so that they can use this software to estimate solutions of ordinary differential equations. On the Resources page you can find additional links to videos which may be helpful.
The sessions are:
- Introduction (August 28, 2018) - Matlab environment, vector addition, cross and dot products, term-by-term multiplication and division, and loops (for). Sequences and convergence review.
- Euler's Method (September 3, 2018) - Work through an example of a first-order differential equation. See when the computation estimates the solution well, and how to tell when the estimate is poor.
- Adaptive Time-Stepping (September 10, 2018) - Use an approximation from Euler's Method at a smaller time step to find the next time step that keeps the approximation within a specified tolerance. While loops are covered here.
- Systems, (September 17, 2018) - Convert a second-order equation to a system of first-order equations, and apply Euler's Method. Functions and handles are introduced here, along with phase plane plots.
- ODE Suite (September 24, 2018) - The last area to decide on a scheme using Matlab's ODE Suite is the property of stiffness. We introduce backward-differencing schemes here, and qualitatively discuss stability of schemes.