Course detail
Numerical methods 2
FAST-DAB035Acad. year: 2024/2025
Mathematical approaches to the analysis of engineering problems, namely ordinary and partial differential equations, directed to numerical calculations - deeper knowledge than from the course DA01.
Language of instruction
Czech
Number of ECTS credits
10
Mode of study
Not applicable.
Guarantor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Entry knowledge
At the level of the course DA61.
Rules for evaluation and completion of the course
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Aims
Getting acquainted with the basics of the theory of numerical solution of ordinary differential equations and systems of such equations and second-order partial differential equations. Learning how to use numeric methods to solve such equations.
Study aids
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
DALÍK J., PŘIBYL O., VALA J.: Numerické metody 2 (pro doktorandy). FAST VUT v Brně 2010. (CS)
Recommended reading
Not applicable.
Classification of course in study plans
- Programme DKA-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-GK Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-GK Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-GK Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-GK Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-V Doctoral 2 year of study, winter semester, compulsory-optional
Type of course unit
Lecture
39 hod., optionally
Teacher / Lecturer
Syllabus
1. Formulation of the initial-value problem in ordinary differential equations of degree 1, basic properties, existence and uniqueness of solutions.
2. Basic numerical methods for the initial-value problems and their absolute stability.
3. Introduction to the variational calculus, basic spaces of integrable functions.
4. Classical and variational formulations of elliptic problems for ordinary differential equations of degree 2, basic physical meanings.
5. Standard finite difference method for elliptic problems for ordinary differential equations (ODE) of degree 2 and its stable modifications.
6. Approximation of boundary-value problems for second order ODE by the finite element method.
7. Classical and variational formulation of elliptic problems for fourth-order ODE and approximation by the finite element method.
8. Classical and variational formulation of elliptic problems for second-order partial differential equations.
9. Finite element method for elliptic problems in second-order partial differential equations.
10. Finite volume method.
11. Discretization of non-stationary problems for second-order differential equations by the method of straight-lines.
12. Mathematical models of flow. Nonlinear problems and problems with dominating convection.
13. Numerical methods for the models of flow.