Category Archives: Mathematica

An earlier post discusses Mathematica code for Euler’s method. Here is some updated code. A couple preliminary notes: I like to clear all variables at the beginning. For systems it is fun to superimpose the plot on top of the … Continue reading →

Here is a simple example of comparing different numerical methods for ODEs. We focus on the example subject to the initial condition . We know that the exact solution is . Let’s compare Euler’s method, the trapezoid method, and the … Continue reading →

Here is a description of how to implement Euler’s method for a system. We focus on a simple example: where and First, let’s put in the functions which define the system Next, we make a StreamPlot of the vectorfield Now … Continue reading →

We use Euler’s method to find an approximate solution to with initial value First, we set (The semi colon just suppresses the output.) Next we define the function Now we set up the recursion relation. We want the initial values … Continue reading →