Materials
The (hand-written) lecture notes can be found below. Most of the lectures roughly follow
D. F. Griffiths and D. J. Higham, Numerical Methods for Ordinary Differential Equations, Springer.
September 9
Introduction of initial value problems for ordinary differential equations. Existence and uniqueness. Continuous dependence on initial data.
Lecture 1
lecture1.pdf579.7KB
September 11
Euler's method: rationale, local truncation error (LTE), global error, weaknesses. (Four Matlab scripts/functions, designed for demonstrating the weaknesses of the Euler's method, are also enclosed.)
ff.m49 bytes
September 16
Linear multistep methods (LMMs): examples, construction and consitency.
September 18
Linear multistep methods: zero-stability and (global) convergence.
September 23
Linear multistep methods: stiff problems, absolute stability, region of absolute stability. (Two Matlab scripts for comparing the explicit and implicit Euler's methods for stiff problems are enclosed.)
September 25
Linear multistep methods: A-stability, absolute stability for systems (n>1), stiff systems.
September 30
Runge-Kutta methods: definition, examples, order conditions.
October 2
Runge-Kutta methods: absolute stability, stability function.
October 7
Runge-Kutta methods: absolute stability for systems (n>1).
October 9
Parabolic PDEs: (Spatial) discretization of a simple model problem, stiffness of the resulting initial value problem.
October 14
Parabolic PDEs: Crank-Nicolson method and its properties. Hyperbolic PDEs: conservation of energy.
October 16
Hyperbolic PDEs: discretization and conservation of "discrete energy".
Some additional reading related to the topic of the course: the lecture notes "Discretizing differential equations" by Timo Eirola and Olavi Nevanlinna.