Numerical Methods 2

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Code Completion Credits Range
01NME2 KZ 2 2+0
Michal Beneš (guarantor)
Michal Beneš (guarantor)
Department of Mathematics

The course is devoted to numerical solution of boundary-value problems and intial-boundary-value problems for ordinary and partial differential equations. It explains methods converting boundary-value problems to initial-value problems and finite-difference methods for elliptic, parabolic and first-order hyperbolic partial differential equations.


Basic course of Calculus, Linear Algebra and Ordinary Differential Equations (in the extent of the courses 01MA1, 01MAB2-4, 01LA1, 01LAB2, 12NMET held at the FNSPE CTU in Prague).

Syllabus of lectures:

I.Numerical solution of ordinary differential equations - boundary-value problems

1.Shooting method

2Method of transformation of a boundary-value problem

3.Method of finite differences

4.Solution of non-linear equations

II.Numerical solution of partial differential equations of the elliptic type

1.Finite-difference method for linear second-order equations

2.Convergence and the error estimate

3.Method of lines

III.Numerical solution of partial differential equations of the parabolic type

1.Method of finite differences for one-dimensional problems

2.Method of finite differences for higher-dimensional problems

3.Method of lines

IV.Numerical solution of hyperbolic conservation laws

1.Formulation and properties of hyperbolic conservation laws

2.Simplest finite-difference methods

Syllabus of tutorials:
Study Objective:


Numerical methods based on transformation of a boundary-value problem to an initial-value problem, finite-difference method for ODE's and PDE's.


Application of given methods in particular examples in physics and engineering including computer implementation and error assessment.

Study materials:

Key references:

[1] A.A. Samarskij, Theory of Difference Schemes, CRC Press, New York, 2001

[2] J.W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer Science & Business Media, 2013

[3] R.J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems, SIAM, 2007

[4] R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002

Recommended references:

[5] E. Godlewski a P.-A. Raviart, Numerical approximation of hyperbolic systems of conversation laws, New York, Springer 1996

Media and tools:

Computer training room with Windows/Linux and programming languages C, Pascal, Fortran.

Time-table for winter semester 2022/2023:
Time-table is not available yet
Time-table for summer semester 2022/2023:
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The course is a part of the following study plans:
Data valid to 2022-12-02
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