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   +(36) 88 624 023 | |    H-8200, Veszprem, Egyetem str. 10, Building I.

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Ferenc Hartung, professor
email: hartung.ferenc@mik,

Topics covered:

Students acquire knowledge related to the special topics of numerical analysis, taking into account their individual training plan and interests. Possible topics:

Fixed point iteration in one and multiple dimensions, order of convergence.

Eigenvalue of matrices, singular value, SVD decomposition. Distribution of the eigenvalues, perturbation of the eigenvalue problem. Power method, Sturm sequence, QR-method.

Spline and trigonometric interpolation, fast Fourier transform.

Optimization (quasi-Newton methods, least square solution of linear systems)

numerical integration (Euler-Maclaurin summation formula, Romberg integration, adaptive quadrature methods, Improper integrals, multiple integrals)

Numerical approximation of ODEs: Runge-Kutta-Fehlberg method, multistep methods, predictor-corrector methods, stiff differential equations. Numerical approximation of boundary value problems using shooting method and finite difference method.

Finite difference method for solving elliptic, parabolic and hyperbolic PDEs.


R. Burden, J. D. Faires, Numerical analysis, Brooks/Cole, 2011.
E. Atkinson, An introduction to numerical analysis, John Wiley and Sons, 1978.
Stoer, R. Bulirsch, Introduction to numerical analysis, Springer-Verlag, New York, 1980.