Scientific Computing

6 EC

Semester 2, period 4

5284SCCO6Y

Owner Master Computational Science (joint degree)
Coordinator dr. G. Závodszky
Part of Master Computational Science (Joint Degree), Master Stochastics and Financial Mathematics, specialization Data Analysis and Statistics, year 1Master Stochastics and Financial Mathematics, specialization Financial Mathematics, year 1Master Stochastics and Financial Mathematics, specialisation Probability and Decision Making, year 1
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Course manual 2024/2025

Course content

The course focuses on developing numerical algorithms to solve prototypical partial differential equations. Students will learn how to discretize differential equations using finite difference approximations, analyse the stability and accuracy of finite difference schemes, and implement these schemes in code to solve a variety of scientific and engineering problems. Topics covered include:

  • Derivation of finite difference formulas for various derivatives
  • Explicit and implicit finite difference methods for ordinary and partial differential equations
  • Stability analysis techniques, such as the Courant–Friedrichs–Lewy (CFL) condition
  • Accuracy and convergence of finite difference schemes
  • Applications to problems such as heat transfer, fluid flow, and wave propagation

Furthermore, the course provides a brief introduction to advanced numerical methods (finite volume, and finite element).

Study materials

Literature

  • Kyle Novak, Numerical Methods for Scientific Computing, 2nd edition

Software

  • A working python distribution is necessary with the basic scientific libraries (numpy, scipy, numba, matplotlib).

Objectives

  • Knowledge. The student has basic knowledge about solving (examples of) partial diferential equations and is able to analyze stability and accuracy of a numerical scheme
  • Skills: The student is able to develop a computational model for solving examples of partial differential equations (e.g wave equation, diffusion equations) in (simple) applications

Teaching methods

  • Lecture
  • Computer lab session/practical training
  • Working independently on e.g. a project or thesis

The lectures will present the theoretical background as well as adding several optional small simulation exercises. During these lectures three assignments will be defined that the students will work on in pairs. The guided laptop sessions will give aid with the technical questions towards the completion of the assignments.

Learning activities

Activity

Hours

Hoorcollege

28

Laptopcollege

28

Tentamen

3

Self study

109

Total

168

(6 EC x 28 uur)

Attendance

This programme does not have requirements concerning attendance (Ter part B).

Assessment

Item and weight Details

Final grade

1 (100%)

Tentamen

lab assignment 50% and exam 50%

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Weeknummer Onderwerpen Studiestof
1
2
3
4
5
6
7
8

Contact information

Coordinator

  • dr. G. Závodszky