Numerical Methods for Ordinary Differential Equations

Garant předmětu:

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Department of Technical Mathematics

Synopsis:

Goal and focus:

Numerical solution of the inital value problem (Cauchy problem) for ODE or system of ODEs.

Numerical solution of the bondary value problems for ODE of the second order.

Basic concepts

Existence

Uniqeness

Stability

Global and truncation errors

Convergence

Consistency.

One step methods

Linear multistep methods

Explicit

Implicit

Especially Runge-Kutta methods

Adams-Bashforth method

Adams-Moulton method

BDF

Predictor-corrector.

BVP problem for second order ODE, shooting method, finite diffrence method, basics of week formulation, Galerkin and Petro-Galerkin method. Applications.

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Study Objective:

Study materials:

Buchanan, J.L.:Numerical Methods and Analysis, 1992, McGraw-Hill.

Brenan, K.E.,Campbell, S.L.,Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, 1989, Elseview.

Haier, E., Wanner, G.:Solving Ordinary Differential Equations II, 1996, Springer-Verlag.

LeVegue, R.J.: Finite Difference Methods for Ordinary and Partial Differential Equations , 2007, SIAM.

Nakamura, S.: Applied Numerical Methods with Software, 1991, Prentice Hall.

Ferzinger J.H.: Numerical Methods for Engineering application, 1998, WILLEY-INTERSCIENCE

Vitásek E.: Numerické metody, 1987 SNTL

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: