2.3 Calculation (Euler’s method)

Course subject(s) 2. Improving the model

Calculation (Euler’s method)

The differential equation for the rainbowfish that we have now, could still be solved by hand. It would give you the analytical solution, which is exact. However, we are not doing that in this course, as we want to focus on the modelling, and not on analytical solution methods. We also do not want to limit our models to equations that can be solved analytically.

So, we will approximate the solutions of the differential equation with a numerical method, and we choose Euler’s method. In the next video, this method is explained.

Euler's method

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In the video you have learned about Euler’s method.

For the general differential equation

the

n

-th step of Euler’s method is given by

in which

Δ t

is some time step you have to choose.

In the following exercises, you are learning the method by doing a few of the steps “by hand”, i.e. using a simple calculator. You will probably get bored with these calculations pretty soon, which is the purpose of the exercises :P. And then on the next page, you will use a computer program to automate these calculations.

The initial value problem to use:

The time step is set to one week, so $Δ t = 7$ days.

Get out your calculator (app) and perform the first steps of Euler’s method.

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