# Course page 2017 (temporary)

### This is a mirror of the Canvas homepage for the fall 2017 edition of SF2520.

### It is intended for students at SU without access to the real homepage.

## SF2520 Applied numerical methods

The overall goal of the course is to give you knowledge and tools about how to formulate, analyze and implement advanced computer methods based on numerical algorithms for solving mathematical models from scientific and engineering applications.

The course covers three main areas: ordinary differential equations (period 1), partial differential equations (period 2) and numerical linear algebra (period 2).

## Course structure

- Lectures

There are 25 lectures in all, with approximately half in period 1 and half in period 2.

Below is a plan for the lectures. The suggested reading are chapters in the course book by L. Edsberg. (The plan is still preliminary.)

#### Period 1

- Course introduction, ODE theory

Lectures 1, 2 (Aug 29, 31)

Reading: chapters 1+2 - Initial value problems

Lectures 3, 4, 5 (Sep 5, 7, 12)

Reading: chapters 3, A2, A3 - Boundary value problems

Lectures 6, 7, 8 (Sep 14, 21, 26)

Reading: chapter 4 - Introduction to PDEs

Lecture 9 (Sep 28)

Reading: chapters 5, 9 - Parabolic PDEs

Lectures 10, 11 (Oct 3, 5)

Reading: chapter 6

**Period 2**-- TBA - Course introduction, ODE theory
- Computer exercises

The students should work on their own with a set of computer exercises on numerical methods.

There are eight computer exercises in the course.

Exercises 1-6 are available in the course book, appendix C. Exercises 7-8 will be available on the homepage as PDF.

The exercises should be done in groups of two students. Each exercise is examined by a short written report and Matlab code. Read about the requirements for the report here. The report and the Matlab code is submitted electronically via the links under Assignments, before the deadlines given below.

*Note:*You only need to submit one report per group, per exercise. However, you should work together in the group and both of you should be able to explain your solution. I may ask some of you for individual oral presentations.Each week there are 1-2 sessions scheduled in the computer labs where students can come and ask questions and get help with the exercises. During the labs we use Stay a While as queuing system for questions (queue name = SF2520). Note, however, that the main part of the work must be done outside class.

Each submitted exercise is given a number of credit points (p), where the maximum of each lab is shown below. The points are added to a total of credit points (Tp), where max of Tp is 31. One point is deducted for a late submission. To pass the computer exercise part of the course, a minimum of 19 Tp is needed with at least 4 Tp from exercises 7 and 8.

#### Exercises

- ODE systems of LCC type and stability

Max 3 points, deadline 12 Sep 2017

Some Q&A:- Can we use ode23 or ode45 in exercise 1?

Answer: no, use expm(A*t) - Shall we compute the eigenvalues in 2a) analytically?

Answer: if you want to, but it is easier to use the eig-function in MATLAB. - Newton's method converges to only one (or two) of the critical points, why?

Answer: you have probably given the jacobian incorrectly.

- Can we use ode23 or ode45 in exercise 1?
- Numerical solution of initial value problem

Max 4 points, deadline 22 Sep 2017 - Numerical solution of boundary value problem

Max 3 points, deadline 2 Oct 2017 - Partial differential equation of parabolic type

Max 5 points, deadline 16 Oct 2017 - Numerical solution of elliptic PDE problems

Max 4 points, deadline TBA - Numerical experiment with the hyperbolic model PDE problem

Max 4 points, deadline TBA - TBA

Max 4 points, deadline TBA - TBA

Max 4 points, deadline Jan 2018

- ODE systems of LCC type and stability
- Project

A larger project which requires knowledge from several areas is done at the end of the course. Project presentations are held in December. More details to follow.

## Course literature

- L. Edsberg,
*Introduction to computation and modeling for differential equations,*2nd edition, Wiley 2015.

This is available at Kårbokhandeln. See also the book homepageThe main differences between the two editions are:

Regarding the first edition of the book:- Addition of Chapter 10, containing all the course projects
- An updated part in Chapter 8, on the wave equation
- An updated version of Computer exercise 6

You can use the old edition as your text book, but keep the differences in mind. For the Project and the last Computer exercise you may need the new book.

- Some description of Matlab, e.g. C. Edlund, Matlab i korthet, or the Dundee MATLAB report.
- Material for the Numerical linear algebra part (TBA).

## Examination

There are three parts of the examination. Each must be passed to finish the course:

- Computer exercises (max 31 points)
*Required:*At least 19 points including at least 4 points from the numerical linear algebra exercises (no 7 and 8). - Project (max 5 points)
*Required:*Oral presentation with at least 3 points score. - Exam (max 29 points)
*Required:*At least 13 points.

The final grade is determined by the sum of the points from the three parts (max 31+5+29 = 65 points) according to the following table:

Fx | E | D | C | B | A |

32-34 | 35-39 | 40-45 | 46-51 | 52-57 | 58-65 |