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Lecturer(s)
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Lysák Jaroslav, Ing. Ph.D.
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Zouvalová Katarína, Ing. Ph.D.
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Course content
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Finite difference method, finite volume method and finite element method for solving boundary problems for ODEs and elliptic PDEs. Direct and iterative methods for discretized problems.
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Learning activities and teaching methods
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Lecture supplemented with a discussion, Students' portfolio, Task-based study method, Individual study, Textual studies, Lecture
- Contact hours
- 39 hours per semester
- Team project (50/number of students)
- 48 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
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| prerequisite |
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| Knowledge |
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| describe linear algebra problems (systems of equations, eigenvalues), approximation of a function (interpolation, least squares method), approximation of a derivative and a definite integral, and an initial value problem for an ordinary 1st order differential equation |
| describe and explain basic numerical methods for solving nonlinear equations |
| Skills |
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| používat počítačový software MATLAB nebo podobný a implementovat základní algoritmy numerických metod |
| formulate and solve basic problems of numerical mathematics using numerical methods, i.e. solve linear and nonlinear equations and their systems, determine eigenvalues, approximate functions in terms of interpolation and L2-approximation, approximate value of derivative and definite integral, solve initial value problem for 1st order ordinary differential equation |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| describe and explain the principle of numerical methods for solving initial and boundary value problems for ordinary and elliptic partial differential equations, namely methods of converting the boundary value problem to the initial value problem, difference methods for boundary value problems, Galerkin type methods and finite element methods |
| Skills |
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| use numerical methods to solve initial and boundary value problems for ordinary differential equations |
| analyze the obtained numerical results |
| discuss convergence of methods (firing method and boundary condition transfer method, finite difference method and integral identity method, Galerkin and Ritz method, finite element method) |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Lecture supplemented with a discussion |
| Textual studies |
| Skills |
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| Task-based study method |
| Students' portfolio |
| Individual study |
| Competences |
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| Task-based study method |
| assessment methods |
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| Knowledge |
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| Oral exam |
| Individual presentation at a seminar |
| Seminar work |
| Skills |
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| Skills demonstration during practicum |
| Individual presentation at a seminar |
| Competences |
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| Individual presentation at a seminar |
| Oral exam |
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Recommended literature
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LEVEQUE, Randall J. Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. Philadelphia, 2007. ISBN 978-0-898716-29-0.
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MÍKA, Stanislav a PŘIKRYL, Petr. Numerické metody řešení eliptických úloh pro PDR. Plzeň: Západočeská univerzita, 2007.
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MÍKA, Stanislav a PŘIKRYL, Petr. Numerické metody řešení okrajových úloh pro ODR. Plzeň: Západočeská univerzita, 2007.
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Reddy, J. N.; Anand, N. K.; Roy, P. Finite element and finite volume methods for heat transfer and fluid dynamics. 2023. ISBN 978-1-00-927548-4.
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STRIKWERDA, John C. Finite difference schemes and partial differential equations. 2nd ed.. Society for Industrial and Applied Mathematics. Philadelphia, 2007. ISBN 978-0-898716-39-9.
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Trangenstein, J. A. Numerical solution of elliptic and parabolic partial differential equations. Cambridge : Cambridge University Press, 2012. ISBN 978-0-521-87726-8.
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