TFADPV003 Numerical methods in physics

Institute of physics in Opava
winter 2021
Extent and Intensity
0/0/0. Type of Completion: dzk.
Guaranteed by
doc. RNDr. Jan Schee, Ph.D.
Prerequisites
Good knowledge of basic chapters of numerical methods in physics is expected:
- Solution of systems of linear equations (LU-decomposition, tridiagonal systems),
- Polynomial interpolation and extrapolation,
- Orthogonal polynomials,
- Numerical integration using Gaussian quadratures,
- Numerical solution of transcendental equations (Brent's method),
- Search for minima of 1D and 2D functions,
- Solution of ordinary differential equations - Runge-Kutha scheme,
- Random number generators.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of the course is to develop knowledge of basic chapters of numerical methods in physics (see Prerequisites of the course) and to gain knowledge of more advanced chapters of numerical methods in physics at the highest level reflecting the current state of research.
Learning outcomes
It depends on the individual study plan of the student.
Syllabus
  • Particular advanced chapters of numerical methods in physics and their content are selected for the content of the course within the individual study plan so that they are directly related to the topic of the dissertation and at the same time suitably complement parts of other compulsory optional courses of the student's individual study plan. The chapters could be, for example:
    - Interpolation using a cubic spline,
    - Ordinary differential equations (Rung-Kuth scheme with   adaptive step, Richardson extrapolation, Bulirsh-Stroyer method, methods based on predictor-corrector),
    - Problems with boundary conditions (shooting method, relaxation methods),
    - Integral equations (Fredholm's equation of the second kind, Volterra's equation),
    - Integro-differential equations (radiant transfer equations),
    - Partial differential equations (classification, FTCS, Leapfrog, Lax-Wendroff, SOR),
    - Monte-Carlo methods of integration, simulation,
    - Numerical solution of Regge-Wheeler equation with boundary conditions and determination of stationary modes.

Literature
  • Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B. P., Numerical Recipes: The Art of Scientific Computing, Cambridge University Press (2007)
  • Hoffman J.D. and Frankel S., Numerical Methods for Engineers and Scientists, CRC Press, Taylor & Francis Group (2001)
  • Hutchinson I. H., A Student‘s Guide to Numerical Methods, Cambridge University Press (2015)
  • Giordano N.J. and Nakanishi H., Computational Physics, Pearson (2005)
Teaching methods
self-study, discussions
Assessment methods
exam
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information

The course is also listed under the following terms winter 2020, winter 2022, winter 2023, winter 2024.
  • Enrolment Statistics (winter 2021, recent)
  • Permalink: https://is.slu.cz/course/fu/winter2021/TFADPV003