Introduction to Modeling and Simulation

7Numerical Methods

7.1 Introduction

In this chapter we discuss numerical methods in simulation [32]. We discuss numerical approximation of both derivatives and integrals of functions and we derive iterative algorithms for numerical solution of ordinary differential equations (ODEs). Matlab has a number of built‐in functions for numerical solution of ODEs. We discuss the most popular of these functions and give some examples of their use. We also give a brief introduction to Simulink, which is Matlab's graphical block‐diagram program for constructing and simulating systems.

Example 7.1

As a first example of an iterative algorithm, suppose that we want to compute the square root of a real number . Note that the square root of is a solution in of the equation

(7.1)

Dividing both sides of Equation (7.1) by , we have

Thus, the square root of satisfies the implicit equation

(7.2) ...