Numerik für ODEs
Numerical Analysis and Dynamical Systems I
J.M. Melenk
Some
desasters attributable to poor numerics.
A few
software bugs with consequences
Mondays 9:00-10:00, Maths 314
Fridays 10:00-11:00, Palmer G01 (moved from Tuesdays)
office hours: when I am in my office (Maths 202) or by appointment
Exercises:
Numerical Examples
- location of the Chebyshev points handout1.pdf
- Runge's example: influence of knot distribution on interpolation error
handout2.pdf
- Matlab-file for interpolation sheet2.m
- the classical Newton-Cotes rules handout3.pdf
- convergence behavior of the trapezoidal rule and Simpson's rule handout4.pdf
- Matlab-file for trapezoidal rule sheet3.m
- partial answers for sheet 3 lsg_sheet3.ps (please report errors!)
- partial answers for sheet 4 lsg_sheet4.ps (please report errors!)
- a Matlab code to compute the Gaussian points and weight for (almost) arbitrary n gauleg.m
- performance of Gaussian quadrature handout6.ps
- an adaptive quadrature handout7.ps
- partial answers for sheet 5 lsg_sheet5.ps (please report errors!)
- the matlab code for problem 2 on sheet 6 sheet6.m
- partial answers for sheet 6 lsg_sheet6.ps (please report errors!)
- partial answers for sheet 7 lsg_sheet7.ps (please report errors!)
- partial answers for sheet 8 lsg_sheet8.ps (please report errors!)
- the matlab code for problem 2 on sheet 8 sheet8.m
Class notes:
Literature:
A book that appears to be in the library is:
-
Numerical mathematics and computing by Ward Cheney and David Kincaid.
A good compendium on numerical methods and numerical analysis is:
- Numerical Mathematics by
Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri, (Springer Verlag)
The course will also lean on:
- Deuflhard, Hohmann: Numerical Analysis in Modern Scientific Computing, Springer Verlag
- Deuflhard, Bornemann: Scientific Computing with Ordinary Differential Equations, Springer Verlag
Public Domain Software:
many Fortran und C packages for solving problems of numerical linear algebra, quadrature,
and ODEs are public domain and can be retrieved from
NetLib.
Many algorithms (and their C/Fortran implementation) are described in the book
Numerical Recipes in C
by
Press, Teukolsky, Vetterling, Flannery.