MSc in Applied Mathematics
Course "Numerical solution of time-dependent PDE's I."


Information for the lectures

• Schedule: weekly, beginning on 12th February. 12.15 - 13.45, 14.00 - 14.45

• Venue: room 4-429 (Southern building)

Information for the practices

• Schedule: weekly, beginning on 13th February. 8.15 - 9.45

• Venue: room 4-429 (Southern building)

Literature

  •   J.W. Thomas: Numerical Partial Differential Equations: Finite Difference Methods, Springer, 2005 (very detailed textbook for self-study)
  •  B. Jovanovic, E. Süli: Analysis of Finite Difference Schemes, Springer, 2014
  •  U.M. Ascher: Numerical Methods for Evolutionary Differential Equations, SIAM, 2008 (modern wtih more topics)
  •  A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics, Springer, 2007. (Section 13.)

Study materials

  •  The slides of the lectures.

  •  The official Hungarian lecture notes is available here.

  •  Hungarian lecture notes for the finite element discretization.

  •  Problems to solve in the exercises Exercise 1.  Exercises 2-3. Exercise 4.  Exercise 5.  Exercise 6.  Exercise 7.  Exercise 8.  Exercise 9.  Exercise 10.  Exercise 11.
      For the last two exercises, you may use these Matlab code in mlx format or in text format and mlx format or in text format .

  •  Codes for the exercises
on basic empirical error analysis and further semidiscretization
a very simple upwind scheme,
finite difference codes for 2D parabolic problems to read and copy-paste
finite difference codes for 2D parabolic problems to run (mlx format)

Information on the evaluation regarding the practice

  •  On 12 May, a written test will take place at the venue of the practice. You should solve here problems independently.

  •  You can use here only the official lecture notes (slides), also its electronic version on your device.

  •  The mark is determined by the coding assignments.
In concrete terms, the exercises per students using Neptun codes:
OAMH6O - Ex1, F1QAFW - Ex2, YF2S0G - Ex3, CLC52C - Ex4, ZQKEX8 - Ex5, A0TJTB - Ex6, JPWNJX - Ex7.
You are allowed to use any (including AI) tool for writing the code, but you should understand your code. I may ask on the details of this. You have to present it in 10 minutes on 14 May between 8.15 and 10.00 at the venue of the lectures. You do not have to write a presentation for this event but you should run your code then.

Information on the exam

  •  In all cases, oral exam. Venue: room 3-705.

  •  For the exams, you should apply through the Neptun system.

  •  You can use a collection of formulas. This can contain at most 20 formulas with a short description (3-4 words).