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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.

Subsections

- Taylor series
- Numerical Schemes
  - Forward-Euler
  - Backward-Euler
  - Exponential Euler
  - The Trapezoidal Rule