714-0927/03 – The numerical solution of ordinary differential equations (NŘODR)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 10 |
| Subject guarantor | RNDr. Břetislav Krček, CSc. | Subject version guarantor | RNDr. Břetislav Krček, CSc. |
| Study level | postgraduate | Requirement | Choice-compulsory |
| Year | | Semester | winter + summer |
| | Study language | Czech |
| Year of introduction | 2013/2014 | Year of cancellation | 2016/2017 |
| Intended for the faculties | FAST, FEI, USP, HGF, EKF, FMT, FBI, FS | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
The principles of the ordinary differential equations numerical solution. The basic one-step and multi-step methods.
Teaching methods
Individual consultations
Other activities
Summary
The intention of the first part of the subject is to make deeper students’ general knowledge about the ordinary differential equations and their systems. In the second (main) part of the subject the numerical solution of the initial problems for the ordinary differential equations and their systems is taught.
Compulsory literature:
Lambert, J.D.: Computational Methods in Ordinary Differential Equations.
London – New York – Sydney – Toronto: J. Wiley and Sons 1973.
Recommended literature:
Henrici, P.: Discrete Variable Methods in Ordinary Differential Equations.
New York – London : J. Wiley and Sons 1962.
Lapidus, L. – Seinfeld, J.H.: Numerical Solution of Ordinary Differential
Equations. New York – London : Academic Press 1971.
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Introduction
Terminology, classification of differential equations (DE) and their systems.
Initial value problems (IVP).
Transformation of higher order DE into systems of first order DE.
Existence and uniqueness of IVP solution.
Lipschitz condition, conditions expressed via partial derivatives.
IVP preconditionality
Numerical methods for IVP solution.
Principles of IVP solution methods.
Euler method.
Method order.
Approximation errors.
Method convergence.
Method order, Euler method order and global error.
Round errors influence and error estimation by half-step method.
One-step methods.
Taylor methods.
Runge-Kutta methods, error estimation.
Multi-step methods.
Linear k-step method.
Discretization error.
Overview of some multi-step methods.
Solution stability, choice of IVP solution method
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Introduction
Terminology, classification of differential equations (DE) and their systems.
Initial value problems (IVP).
Transformation of higher order DE into systems of first order DE.
Existence and uniqueness of IVP solution.
Lipschitz condition, conditions expressed via partial derivatives.
IVP preconditionality
Numerical methods for IVP solution.
Principles of IVP solution methods.
Euler method.
Method order.
Approximation errors.
Method convergence.
Method order, Euler method order and global error.
Round errors influence and error estimation by half-step method.
One-step methods.
Taylor methods.
Runge-Kutta methods, error estimation.
Multi-step methods.
Linear k-step method.
Discretization error.
Overview of some multi-step methods.
Solution stability, choice of IVP solution method
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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