714-0927/02 – 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 introduction2007/2008Year of cancellation2012/2013
Intended for the facultiesFMT, HGF, EKF, FS, USP, FBI, FAST, FEIIntended 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 Credit and Examination 0+0
Part-time Credit and 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.

Additional study materials

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

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: 2007/2008 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51 0
        Examination Examination 100  51 3
        Exercises evaluation Credit   0
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2012/2013 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2012/2013 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2011/2012 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2009/2010 (P3607) Civil Engineering (3607V025) Theory of Contruction K Czech Ostrava Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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