Aims & Learning Objectives:
Aims: To teach an understanding of linear stability theory and its application to ODEs and evolutionary PDEs.
Objectives:
The students should be able to analyse the stability and convergence of a range of numerical methods and assess the practical performance of these methods through computer experiments.
Content:
Solution of initial value problems for ODEs by Linear Multistep methods: local accuracy, order conditions; formulation as a one-step method; stability and convergence.
Introduction to physically relevant PDEs. Well-posed problems. Truncation error; consistency, stability, convergence and the Lax Equivalence Theorem; techniques for finding the stability properties of particular numerical methods.
Numerical methods for parabolic and hyperbolic PDEs.
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