Introduction

Many engineering applications describe the evolution of some process with time. In order to define such an application we require two distinct pieces of information: we need to know what the process is and also when or where the application started.

In this Section we begin with a discussion of some of these so-called initial value problems . Then we look at two numerical methods that can be used to approximate solutions of certain initial value problems. These two methods will serve as useful instances of a fairly general class of methods which we will describe in Section 32.2.

Prerequisites

• revise the trapezium method for approximating integrals in HELM booklet  31.2
• review the material concerning approximations to derivatives in HELM booklet  31.3

Learning Outcomes

• recognise an initial value problem
• implement the Euler and trapezium $$ method to approximate the solutions of certain initial value problems