1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
The aim of the course is to introduce classical and modern methods of solving of linear and nonlinear partial differential equations. In the course the methods of finite differences, finite volumes and finite elements will be studied and implemented on a computer.

COURSE DESCRIPTION AND SYLLABUS:
1. The finite difference method. Application to linear parabolic and hyperbolic equation in one spatial dimension. Introduction of the concepts of transport and diffusion and t their numerical approximation. Treatment of boundary conditions. Concepts of consistency, stability and convergence. Lax-Richtmyer's equivalence theorem. CFL stability condition for the hyperbolic equation. Overview of the basic schemes and their stability. The practical part involves creating small applications in any programming language.
2. Finite volume method. Principles of discretization on a general and structured meshes. Applications to hyperbolic conservation laws, elliptical and parabolic equations. Comparison with the finite differentiation method. The practical part involves the implementation on the computer of the use of special libraries.
3. The finite element method. Introduction of the method on an elliptical boundary value problem. The principle of variational approximation, Lax-Milgram's lemma and the problem of interpolation. Lagrange finite elements, numerical integration and convergence of continuous finite element method. Application to parabolic problems by the method of lines and an application of finite difference method to the time derivative. Implementation of the method on a computer by using specialized libraries.

1. Finite Volume Methods for Hyperbolic Problems, R. LeVeque, Cambridge Texts in Applied Mathematics, Cambridge University Press, 2002.
2. Numerical Approximation of Partial Differential Equations, A. Quateroni, A. Valli, Springer Series in Computational Mathematics Vol. 23, Springer Verlag, 1994.
3. Numerical Partial Differential Equations, Finite Difference Methods, J. W. Thomas, Springer Verlag, 1995.

Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Izborni modul D - Znanstveno računanje, 2. godina - Regular study - Computer Science and Mathematics
Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Izborni modul D - Znanstveno računanje, 2. godina - Regular study - Computer Science and Mathematics
Ostali izborni predmeti - Regular study - Computer Science and Mathematics