Teaching schedule
The teaching schedule for this part of the unit is shown in Table 1.
Table 1 Teaching schedule
Week |
Date (w/c) |
Lecture |
Lab
|
|---|
1 |
30/09/2024 |
Ordinary Differential Equations (ODE):
Definition of an IVP, the Taylor series, the Euler method, error analysis, solving higher order ODEs |
Exercise 1.1 to Exercise 1.4 |
2 |
07/10/2024 |
Explicit Runge-Kutta Methods (ERK):
Definition of a Runge-Kutta method, the Butcher tableau, derivation of the an ERK method, deriving the order conditions using trees, Derivation of the RK4 method |
Exercise 2.1 to Exercise 2.6 |
3 |
14/10/2024 |
Explicit Runge-Kutta Methods (ERK) cont:
Solving IVPs using ERK methods |
Exercise 2.7 to Exercise 2.10 |
4 |
21/10/2024 |
Explicit Runge-Kutta Methods (ERK) cont:
Adaptive step size control |
Exercise 2.11 |
5 |
28/10/2024 |
Implicit Runge-Kutta Methods (IRK):
Order of an IRK method, deriving IRK methods, solving IVPs using IRK methods |
Exercise 3.1 to Exercise 3.4 |
6 |
04/11/2024 |
Stability:
Definition of stability, stiffness, stability functions, absolute stability, plotting the region of absolute stability, A-stability |
Exercise 4.1 to Exercise 4.4 |
7 |
11/11/2024 |
Boundary Value Problems (BVP):
The shooting method, the finite-difference method |
Exercise 5.1 to Exercise 5.5 |
8 |
18/11/2024 |
Matrix Decomposition Methods:
LU decomposition, solving systems using LU decomposition, LU decomposition with partial pivoting, Cholesky decomposition |
Exercise 6.1 to Exercise 6.3 |
9 |
25/11/2024 |
Matrix Decomposition Methods cont.:
QR decomposition, calculating eigenvalues using the QR algorithm |
Exercise 6.4 to Exercise 6.5 |
10 |
02/12/2024 |
Indirect methods:
Jacobi, Gauss-Seidel and SOR methods, convergence of indirect methods |
Exercise 7.1 to Exercise 7.6 |
11 |
09/12/2024 |
Consolidation and exam preparation
Coursework deadline 9pm on 16/12/2024 |
|