Numerical Solution of Ordinary and Partial Differential Equations

Course guarantor:

Jan Halama

Lecturer:

Luděk Beneš, Jan Halama

Tutor:

Luděk Beneš, Jan Halama

Supervisor:

Department of Technical Mathematics

Synopsis:

Course covers the overview of clasical numerical methods for the solution of evolution problems for ODEs and PDEs. 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 PDEs (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 ODEs.

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 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed
Thu	roomT4:C2-436 Beneš L. 09:45–11:30 (lecture parallel1) Dejvice
Fri

The course is a part of the following study plans:

• 13 136 NSTI MMT 2012 základ (compulsory course in the program)