The present text tries to show, by means of examples coming from diퟎerent corners
of physics, how physical and mathematical questions can be answered using a com-
puter. Nowadays, theoretical physicists are mainly concerned with two subjects: one
is the devising of models, normally in the form of diퟎerential equations, ordinary or
partial, while the other one is their approximate solution, normally with the help of
larger or smaller computers. In a certain way, computational physics can be seen as
the link between theory and experiment. The often involved equations need a numeri-
cal treatment, usually in connection with certain simplifications and approximations.
Once the code is written, the experimental part begins. A computer on which, for in-
stance, a turbulent pipe flow is simulated, can to some extent be regarded as a test
station with easy access to output values such as flow rates, velocities, temperatures,
and also to input parameters like material constants or geometric boundary condi-
tions
Author(s): Michael Bestehorn
Publisher: De Gruyter
Year: 2018
Language: English
Pages: 331
Contents......Page 6
1. Introduction......Page 12
2. Nonlinear maps......Page 23
3. Dynamical systems......Page 51
4. Ordinary differential equations I, initial value problems......Page 69
5. Ordinary differential equations II, boundary value problems......Page 128
6. Partial differential equations I, basics......Page 155
7. Partial differential equations II, applications......Page 204
8. Monte Carlo methods (MC)......Page 251
A. Matrices and systems of linear equations......Page 281
B. Program library......Page 295
C. Solutions of the problems......Page 301
D. README and a short guide to FE-tools......Page 321
Index......Page 328
