Czech

10

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Institute of Mathematics and Descriptive Geometry (MAT)

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At the level of the course DA61.

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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.

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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.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

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39 hours, optionally

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.