Chapter 5Variation: Numerical Integration
Learning Objectives
- Calculate the numerical solutions to sets of ODEs using the Euler, midpoint, and Runge–Kutta methods
- Approximate the error of these methods using a Taylor series expansion
- Understand the sensitivity of each method to the time-step size and how this sensitivity relates to the method order
We conclude our exploration of methods for solving ODEs by discussing numerical methods. Even a few years ago, I would have been tempted to cover this entire chapter with two short sentences:
Open MATLAB on your computer.
Type “help ode45” at the command line.
In other words, the methods I am about to describe have already been implemented in MATLAB, so why do you need to learn them? The first ...
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