Teaching schedule

The teaching schedule for the Runge-Kutta methods part of the module is shown below

Week	Date (w/c)	Lecture	Lab
1	29/09/2025	Ordinary Differential Equations (ODE): Definition of an IVP, the Euler method, error analysis, solving higher order ODEs	Exercise 1.1 to Exercise 1.3
2	06/10/2025	Explicit Runge-Kutta Methods (ERK): general form 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	13/10/2025	Explicit Runge-Kutta Methods (ERK) cont: Solving IVPs using ERK methods	Exercise 2.7 to Exercise 2.10
4	20/10/2025	Explicit Runge-Kutta Methods (ERK) cont: Adaptive step size control	Exercise 2.11
5	27/10/2025	Implicit Runge-Kutta Methods (IRK): Order of an IRK method, deriving IRK methods, solving IVPs using IRK methods	Exercise 3.1 to Exercise 3.3
6	03/11/2025	Stability: Definition of stability, stability functions, absolute stability, plotting the region of absolute stability, A-stability	Exercise 4.1 to Exercise 4.4
7	10/11/2025	Boundary Value Problems (BVP): The shooting method, the finite-difference method	Exercise 5.1 to Exercise 5.5
8	17/11/2025	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	24/11/2025	Matrix Decomposition Methods cont.: QR decomposition, calculating eigenvalues using the QR algorithm	Exercise 6.4 to Exercise 6.5
10	01/12/2025	Indirect methods: Jacobi, Gauss-Seidel and SOR methods, convergence of indirect methods	Exercise 7.1 to Exercise 7.6
11	08/12/2025	Consolidation and exam preparation Coursework deadline 9pm on 16/12/2025