Methods of Time Discretization

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course is devoted to a universal and very effective method for solving problems involving time, the so-called evolutionary problems, especially for partial differential equations with a time variable. This method represents a modern approach to modeling and solving engineering tasks. These problems, both linear and non-linear, model events in many engineering fields, such as heat conduction, oscillations, also in rheology and other parts.

Requirements:

The course is suitable for students of master's and bachelor's study programs, especially those interested in engineering processes. It is taught in an accessible form with many examples and does not require any special prior knowledge. Individual terms are explained from the very basics and the explanation is adapted to the students who enroll in the subject.

Syllabus of lectures:

Basic concepts. Overview and development of computational analytical and numerical methods.

An illustrative introductory simple example explaining the principle of the time discretization method. Algorithms.

Basic properties of function spaces.

Orthogonal and orthonormal systems.

Properties of operators.

Energy functional.

Sobolev spaces.

Classic, generalized and weak solutions.

Integral identity.

Error estimates.

Syllabus of tutorials:

The course syllabus is based on the lecture syllabus

Study Objective:

Students are introduced to all the basics necessary to understand the formulation and modeling of engineering tasks, with an overview of solution methods, as well as the practical and theoretical foundations of methods for solving time-dependent, linear and non-linear tasks.

Study materials:

The basic study material is the course lectures.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Stavební inženýrství, obor Konstrukce pozemních staveb (compulsory elective course)
• obor Konstrukce a dopravní stavby, zaměření Inženýrské konstrukce (compulsory elective course)
• obor Konstrukce a dopravní stavby, zaměření Dopravní stavby (compulsory elective course)
• Stavební Inženýrství - konstrukce a dopravní stavby, specializace Inženýrské konstrukce (compulsory elective course)
• Stavební Inženýrství - konstrukce a dopravní stavby, specializace Dopravní stavby a geotechnika (compulsory elective course)
• Stavební inženýrství - pozemní stavby, specializace Projektování pozemních staveb (compulsory elective course)
• Stavební inženýrství - pozemní stavby, specializace Statika pozemních staveb (compulsory elective course)