In Week 11 we will introduce the concept of absolute stability and see how it applies to the numerical methods for ODE that we have seen so far. We will then introduce linear multistep methods: these are methods that take into account information from previous iterates (not just the last one). In particular, we will study the Adams Moulton and Adams Bashforth methods and investigate their performance.

Intended Learning Outcomes

At the end of the week you should be able to:

  • analyse the performance of both classes of methods in terms of speed, accuracy, and stability
  • explain the difference between Adams Bashforth and Adams Mouldon methods
  • combine Adams Bashforth and Adams Mouldon methods and analyse the resulting error

Tasks and Materials

  • Lectures 19 and 20 are available on the Lectures page.
  • Problem sheet 8 is available and will be discussed in Week 11, please have a look at it before class!