Introduction

In the previous Section we saw two methods (Euler and trapezium) for approximating the solutions of certain initial value problems. In this Section we will see that those two methods are special cases of a more general collection of techniques called linear multistep methods. Techniques for determining the properties of these methods will be presented.

Another class of approximations, called Runge-Kutta methods, will also be discussed briefly. These are not linear multistep methods, but the two are sometimes used in conjunction.

Prerequisites

• review Section 32.1

Learning Outcomes

• implement linear multistep methods to carry out time steps of numerical methods
• evaluate the zero stability of linear multistep methods
• establish the order of linear multistep methods
• implement a Runge-Kutta method

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