MATH7016: Week 9

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..