714-0927/03 – The numerical solution of ordinary differential equations (NŘODR)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantorRNDr. Břetislav Krček, CSc.Subject version guarantorRNDr. Břetislav Krček, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2013/2014Year of cancellation2016/2017
Intended for the facultiesFS, USP, FMT, FEI, FAST, HGF, FBI, EKFIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC20 RNDr. Břetislav Krček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 0+0
Combined Examination 0+0

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

Další požadavky na studenta

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

Full-time form (validity from: 2013/2014 Winter semester, validity until: 2016/2017 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2014/2015 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner