Solving a System of ODEs

TensorFlow can be used for many algorithmic implementations and procedures. A great example of TensorFlow's versatility is implementing an ODE solver. Solving an ODE numerically is a iterative procedure that can be easily described in a computational graph. For this recipe, we will solve the Lotka-Volterra predator-prey system.

Getting ready

This recipe will illustrate how to solve a system of ordinary differential equations (ODEs). We can use similar methods to the previous two sections to update values as we iterate through and solve an ODE system.

The ODE system we will consider is the famous Lotka-Volterra predator-prey system. This system shows how a predator-prey system can be oscillating, given specific parameters.

The Lotka-Volterra system was published in a paper in 1920 (see also 1). We will use similar parameters to show that an oscillating system can occur. Here is the system represented in a mathematically discrete way:

Here, X is the prey and Y will be...