Course detail
Numerical methods II
FAST-DA63Acad. year: 2020/2021
Numerical methods for the initial-value problem for one ordinary differential equation (ODE) of order one and for systems of ODE of order one, absolute stability, variational formulation of boundary-value problems for ODE and partial DE of order two, discretization of elliptic differential problems by the finite difference and the finite element methods, numerical methods for the non-stationary parabolic and hyperbolic differential problems, numerical solution of a nonlinear differential boundary-value problem.
Supervisor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Learning outcomes of the course unit
Not applicable.
Prerequisites
Differential and integral calculus of one- and two-functions, interpolation and approximation of functions, numeric differentiation and intgration, numerical linear algebra.
Co-requisites
Not applicable.
Recommended optional programme components
Not applicable.
Recommended or required reading
Not applicable.
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
Not applicable.
Language of instruction
Czech
Work placements
Not applicable.
Course curriculum
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.
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.
Specification of controlled education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Classification of course in study plans
- Programme D-K-E-SI (N) Doctoral
branch PST , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch PST , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-SI (N) Doctoral
branch PST , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-SI (N) Doctoral
branch PST , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch MGS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-E-SI (N) Doctoral
branch MGS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-SI (N) Doctoral
branch KDS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-SI (N) Doctoral
branch KDS , 2. year of study, winter semester, 10 credits, compulsory-optional
branch MGS , 2. year of study, winter semester, 10 credits, compulsory-optional - Programme D-P-C-SI (N) Doctoral
branch MGS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch FMI , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-E-SI (N) Doctoral
branch FMI , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-SI (N) Doctoral
branch FMI , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-SI (N) Doctoral
branch FMI , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch KDS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-E-SI (N) Doctoral
branch KDS , 2. year of study, winter semester, 10 credits, compulsory-optional
branch VHS , 2. year of study, winter semester, 10 credits, compulsory-optional - Programme D-P-C-SI (N) Doctoral
branch VHS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch VHS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-SI (N) Doctoral
branch VHS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-GK Doctoral
branch GAK , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-GK Doctoral
branch GAK , 2. year of study, winter semester, 10 credits, compulsory-optional