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# Numerical Integration

### Student Objectives for this Chapter

• Understand the Process of Numerical Integration using Euler's method
• Understand some of the other Numerical Integration Methods (algorithms)
• Consider the Reasons for Choosing One Method over Another
Pharmacokinetics involves rate processes. Rate process are readily described with differential equations. With a diagram for a pharmacokinetic model with its circles and arrows you should now be able to write the corresponding differential equations. Thse differential eqautions can be integrated analytical by various methods. We have used the Laplace transform method as it can be applied to many of the equations found in pharmacokinetics. There are a few types of differential equations which can't be integrated and often it is just easier to let the computer do the integration for you. The computer takes the slope or rate of change or differential equation for a component and a starting point to get to a new value. Euler's method is a simple point and slope method that is relatively easy to understand. We will start by exploring this method in some detail before moving on to some other, more efficient methods.

These methods include

• Point-slope Methods
• Euler's Method
• Runge-Kutta Methods
• RKF45 Method
• Multi-steps Methods
• Predictor-Corrector Methods