Core04: Computational Techniques - Archived material for the year 2019-2020

2019-2020
Lecturer(s): 
Prof. Yuji Nakatsukasa
Course Term: 
Michaelmas
Course Overview: 

Computational Techniques will introduce a number of key methods for studying continuum models. The first week will focus on the basics and applications of numerical linear algebra, treating linear systems, eigenvalue problems and the singular value decomposition (SVD). On the second week we treat finite differences and finite element methods for solving differential equations, showing how to derive the corresponding mathematical model. We then use these models as vehicles to demonstrate the relevant analytical and computational methods. At the end of each week, the students will have the complete set of tools needed to set up, analyse and solve a class of mathematical models.

Course Syllabus: 

SVD, eigenvalues, linear systems, Krylov subspace methods, randomized algorithms

Finite difference methods, error analysis, stability analysis, stiff problems. Multidimensional finite difference and finite element methods for elliptic problems. Finite element and discontinuous Galerkin methods.

Reading List: 

P. E. Farrell, Finite Element Methods for PDEs, C 6.4 course lecture notes
R. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007
E. Süli and D. Mayers, An Introduction to Numerical Analysis, CUP 2003
L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM 1997

Please note that e-book versions of many books in the reading lists can be found on SOLO and ORLO.