Introduction to PDEs and Numerical Methods

Introduction to PDEs and Numerical Methods

General Information

Lecturer Dr. Joachim Rang


Assistant


Schedule Lecture: Wed 9:45-11:15 in room HS 65.4 (GITZ)


Exercises: Friday 13:15-14:45 in room HS 65.4 (GITZ)


Start 23.10.2014


Prerequisites Basic courses up to the intermediate diploma


Target group Students of computer science, mathematics, natural or engineering sciences or guest students in their advanced study period, CSE students


Certificates Homework assignments and active participation in the exercises, tests


Office hours by arrangement


Extra tutorial Friday, 13.02.2015, 15:00-16:00 in HS 65.4


Exam Tuesday, 01.09.2015, 10:15-11:45 in PK 2.1


Literature:

A script for the lecture is available HERE.

To download books and papers here: http://www.biblio.tu-bs.de/semapp/, click on Prof. Hermann G. Matthies "Introduction to PDEs and Numerical Methods" and "Numerical methods for PDEs" and then on the corresponding buttons "Volltext anzeigen"

Lecture slides

Homework assignments:

To obtain full points explain your solutions thoroughly and self-consistently with all necessary intermediate conclusions and calculation steps as to leave no doubt about the correctness and your understanding. Structure programmes nicely and with comments and argue why you think that it works. Support your reasons with necessary plots, examples, etc. so that it becomes obvious.

  • Assignment 1 (Introduction to PDEs, deadline: 12:00 o'clock, Wednesday - 29.10.2014)
  • Assignment 2 (Analytical solution to ODEs, deadline: 12:00 o'clock, Wednesday - 05.11.2014)
  • Assignment 3 (Finite difference schemes 1D, deadline: 12:00 o'clock, Wednesday - 12.11.2014)
  • Assignment 4 (FD approximation of the Poisson equation, deadline: 12:00 o'clock, Wednesday - 19.11.2014)
  • Assignment 5 (Fourier series, deadline: 12:00 o'clock, Wednesday - 26.11.2014)
  • Assignment 6 (Elliptic equations, deadline: 12:00 o'clock, Wednesday - 03.12.2014)
  • Assignment 7 (FD shemes on non-equidistent grids, compact schemes , deadline: 12:00 o'clock, Wednesday - 10.12.2014, further Informations)
  • Assignment 8 (Time discretisation methods, deadline: 12:00 o'clock, Wednesday - 17.12.2014, Butcher tables)
  • Assignment 9 (Analytical solution of heat equation, deadline: 12:00 o'clock, Wednesday - 7.1.2015)
  • Assignment 10 (Numerical solution of heat equation, deadline: 12:00 o'clock, Wednesday - 14.1.2015)
  • Assignment 11 (Analytical solution of spatially 1D hyperbolic equations, ATTENTION: assignment is corrected on the 21.01 -correction: Excercise 1, third PDE, initial condition (dot instead of prime), deadline: 12:00 o'clock, Wednesday - 21.1.2015)
  • Assignment 12 (Numerical solution of hyperbolic equations: 12:00 o'clock, Wednesday - 28.1.2015)
  • Assignment 13 (Numerical solution of 2D elliptic eqautions: 12:00 o'clock, Wednesday - 04.2.2015)

Sketch of tutorials :

  • Tutorial 1 (Introduction, differential operators, classification of PDEs)
  • Tutorial 2 (Analytical solution of the 1D Poisson equation)
  • Tutorial 3 (Finite difference method in 1D)
  • Tutorial 4 (Finite difference method in 1D, convergence, consistence, stability)
  • Tutorial 5 (Eigenvalues of ODEs, Fourier-transform)
  • Tutorial 6 (Elliptic equations - existence and bounds of solution, FD discretization)
  • Tutorial 7 (FD on non-equidistant grids, higher order schemes)
  • Solving Initial value problems (time integration schemes)
  • Tutorial 8 (The heat equation: numerical schemes and their consistency/stability analysis)
  • Tutorial 9 (Numerical solution of the inhom. heat equation with different time integration schemes, analytical solution of advection problems)
  • Tutorial 10 (Numerical solution of hyperbolic equations)
  • Tutorial 11 (2D Elliptic equations)
  • Tutorial 12 (Seperation of vriables)

Additional information can be found in StudIP. The links below work only if you are logged into StudIP.

  • Assignment 6 (Elliptic equations, deadline: 12:00 o'clock, Wednesday - 03.12.2014)