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Course: Numerical methods for physicists 2

Department/Abbreviation: SLO/NMF2

Year: 2020

Guarantee: 'Ing. Jaromír Křepelka, CSc.'

Annotation: The aim consists in demonstration of methods for solution of ususal nad partial differential equations, discrete and quick Fourier transforms, representation using the sparse matrices and special functions.

Course review:
1. Numerical solutions of ordinary differential equations - problem with initial condition (Euler method, Runge-Kutta methods, Merson method, automatic choice of integration step, implicit integration methods, stability convergence, correctness), boundary problem (method of shooting, linear systems of differential equations, analytical solutions, problems of existence of numerical solutions, construction of difference schemes, Marcuk identity). 2. Discrete and fast Fourier transform and its applications. 3. Solution of partial differential equations - boundary and initial value problems, final difference methods, finite element methods, variational principle, Galerkin method, spectral methods. 4. Algorithms for manipulation with Sparse matrices - representation and methods. 5. Random numbers - pseudo-random number generation, uniform distribution, normal distribution. 6. Special functions - gamma function, beta function, factorials, binomial coefficients, error function, exponential integrals, Bessel functions, Airy function, Fresnel integrals.