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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Numerical Solution of Ordinary and Partial Differential Equations

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Code Completion Credits Range Language
2013030 Z 2 2P+0C Czech
Lecturer:
Jan Halama
Tutor:
Jan Halama
Supervisor:
Department of Technical Mathematics
Synopsis:

Course covers the overview of clasical numerical methods for the solution of evolution problems for ODE’s and PDE’s. Students get familiar with discretization errors, stability of schemes and convergence of solution. Emphasis is put on a practical use of numerical methods (choice of method, discretization, ...).

Requirements:
Syllabus of lectures:

Overview of numerical methods for initial value problems for ODE.

• Types of errors in numerical solution. Order of accuracy.

• Stability and convergence.

• Higher order methods. Multi-step methods.

• Absolute stability.

• Numerical methods for stiff problems.

• Numerical schemes for evolution PDE‘s (diffusion equation, wave equation, transport equation).

• Stability, convergence, approximation for finite difference method.

• Spectral criterion of stability.

• Method of lines, link to the solution of systems of ODE’s.

• Solution of stationary problems using iterative methods (Laplace and Poison equation).

• Extensions for multi-dimensional cases, ADI methods.

• Basic principles of finite volume method.

Syllabus of tutorials:
Study Objective:
Study materials:

R. le Veque: Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems, SIAM, 2007

J. W. Thomas: Numerical Partial Differential Equations: Finite Difference Methods, Springer, 1995

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-01-19
For updated information see http://bilakniha.cvut.cz/en/predmet1896506.html