## Week 9

We did a little revision of the earlier material.

In VBA we will look at finite difference methods for Laplace’s Equation.

## Week 10

We will look at finite differences for the Heat Equation.

In VBA we will implement same.

## Week 11 — 2nd 20% VBA Assessment

In class we will do a survey of advanced methods including:

- Multi-Step Methods for ODE’s including Milne’s Method and the Adams-Moulton Method
- Systems of ODEs. Convergence and stability. Eigenvalue Problems.
- Derivative boundary conditions for PDEs.
- Irregular Boundaries.
- The ADI Method.

The VBA 20% Assessment 2 will be based on

- Runge-Kutta for IVPs
- Shooting Method for BVPs
- Finite Difference Method for Laplace’s Equation

## Week 12 – 40% Written Test (with aid of Excel).

The 40% assessment will take place in the VBA lab time. The two class times will be given over as tutorials.

It will be based on everything we have studied:

- Everything up to fourth-order Runge-Kutta (including Euler and Heun by hand and theoretical questions for higher order RK)
- Second Order IVPs
- Boundary Value Problems — shooting method and finite differences
- Laplace’s Equation using Finite Differences
- Heat Equation using Finite Differences

## Study

Study should consist of

- doing exercises from the notes
- completing VBA exercises

## Student Resources

Please see the Student Resources tab on the top of this page for information on the Academic Learning Centre, etc..

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