# Timetable

This schedule is not final but this is the anticipated curriculum of TMA4212.

JCS = John C. Strikwerda's book on finite differences

SM = Suli and Mayers, An introduction to Numerical Analysis

N = course note This note is still under construction (especially chapter 7). Please let me know of any mistakes you find.

#### Prerequisites

Subject Topics subtopics
Linear algebra Basics Vector and matrix norms; Symmetric Positive Definite matrices; Inner product spaces; Linear independence; basis of a vector space; orthonormal basis.
Matrix factorizations Diagonalization and orthogonal diagonalization of matrices; LU decomposition (Gaussian elimination, pivoting); Cholesky factorization; QR factorization; SVD; Jordan Canonical form; Schur factorization.
Topics of interest in numerical linear algebra Spectral radius; Gershgoring's theorem; Condition number; Neumann series.
Iterative methods Newton method; fixed point iteration; convergence of the basic iterative methods (Jacobi, Gauss-Seidel and SOR) for linear systems.
Calculus Taylor theorem
Solution of ODEs Numerical methods for ODEs. Runge-Kutta and multistep, implementation, stability analysis, order conditions, convergence of the Euler method.

### Timetable

Week Date JCS and SM N Subject Read on your own Some relevan exam questions
2 05.01, 09.01 ch. 1-2,3 Introduction to the course. Difference operators and difference formulae. Boundary value problems. Ch. 1, last part of Ch 3.1.2, beginning of Ch. 3.2, Ch. 3.3. Problem 1a, 1b, 1c, May 2009. Problem 5, June 2014.
3 12.01, 16.01 4.1-4.5 Classification of linear PDEs. Methods for parabolic problems. Forward Euler, Backward Euler and Crank-Nicholson. LTE of the theta-method. Method of lines. Problem 3a) exam June 2010.
4 19.01, 23.01 6 Methods for elliptic equations. Exercise 1, exam June 2010. Problem 2, August 2014. Problem 2, June 2014.
5 26.01, 30.01 7.1–7.4. Methods for advection equations and hyperbolic systems. CFL condition. Problem 4 August 2014.
6 02.02, 06.02 7.5–7.6. 5.1–5.4, 5.6 Advection equations and hyperbolic systems. Stability of parabolic problems. Problem 3 June 2012.
7 09.02, 13.02 5.6, 5.8, 5.9 Matrix stability. Lax equivalence theorem. Von Neumann stability. 5.5 is not part of the curriculum. 5.7 is not part of the curriculum. Problem 4 Exam May 2013. Ch. 5.4 note. Example page 61-62 note. Problem 3, Exam May 2013.
8 16.02, 20.02 7.6, 7.7 More on von Neumann stability. Dissipation and dispersion. Ex.1b May 2004, Ex.3c June 2007, Ex.3c June 2010, Ex.2b May 2011, Ex.1b Aug 2011, Ex.3b Aug 2014, Ex. 3c June 2006
9 23.02, 27.02 6 Elliptic equations maximum principle. Project work. Pb 2 August 2014. Pb 4 May 2013.
10 02.03, 06.03 13 JCS p 339-349 p 354-356 Numerical solution of linear systems. Pb 3 June 2013
11 09.03, 13.03 Project work.
12 16.03, 20.03 Project work and presentation. Numerical linear algebra.
13 23.03, 27.03 14 JCS p 373-387 p 390-391 Pb 2c Aug 2013, Pb 2 May 2013, Pb 1c Aug 2014
15 10.04 14 SM p 385-399 Finite element method: Rayleigh–Ritz and Galerkin principles and methods. Pb 1: May 2009, May 2011, May 2013, Aug 2013, June 2014, Aug. 2014.
16 13.04, 17.04 SM chaper 14 p 385-399. See material in It's learning. Finite element method. Error estimastes (from Suli and Mayers). 2D Poisson equation. Exam problems. Pb2 June 2010, Pb2 Aug 2011, Oppg 2 Aug 2012, Oppg 4 June 2012.