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Numerical Preliminaries

In this first section we will shortly introduce some fundamental concepts without going to deep into the mathematical details. This will help you understand how hsolve relates to the software design of Genesis and why it is superior when compared to the other objects.

The basic problem can be stated as follows:

  1. A biological model - what we want to compute - is a set of coupled biological components.
  2. The time-dependent behavior of a biological component is described with a (set of) differential equation(s).
  3. A single differential equation describes a rate of change of a variable.

To solve a system of differential equations that describes the behavior of a biological system, we use a numerical method. The methods about to be introduced are all based on the Taylor series.