Numerical Metods for Quantum Technologies
Code  Completion  Credits  Range 

D01NMQ  ZK  2P 
 Garant předmětu:
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 Department of Mathematics
 Synopsis:

The course is devoted to numerical solution of boundaryvalue problems and intialboundaryvalue problems for ordinary and partial differential equations. It explains methods converting boundaryvalue problems to initialvalue problems, finitedifference and finitevolume methods for elliptic, parabolic and firstorder hyperbolic partial differential equations. Some methods based on stochastic or particle approach are discussed as well.
 Requirements:
 Syllabus of lectures:

I. Finite difference method1. case of stationary equations of mathematical physics2. case of transient equations of mathematical physicsII. Finite volume method1. principle of the method2. application for transport problemsIII. Finite element method1. case of stationary equations of mathematical physics2. case of transient equations of mathematical physicsIV. Stochastic and particle method1. Monte Carlo Method2. Molecular dynamics
 Syllabus of tutorials:
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 Study materials:

Key references:[1] J.W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer, 2013.[2]S. C. Brenner a L. Ridgway Scott, The mathematical theory of finite element methods, New York, Springer 1994.[3]S. Mazumder, Numerical Methods for Partial Differential Equations Finite Difference and Finite Volume Methods, Elsevier Science Publishing, 2016.[4]R. J. LeVeque, Numerical methods for conservation laws, Basel Birkhäuser 1992.[5]M. Feistauer: Mathematical Method in Fluid Dynamics, Longman, 1993.Recommended references:[6]S.M. Becker, ed., Modeling of Microscale Transport in Biological Processes, Elsevier, Amsterdam 2017.[7]A. R. Leach. Molecular Modelling: Principles and Applications, Prentice Hall, 2nd edition, 2001.[8]C.Robert, G.Casella, Monte Carlo Statistical Methods, Springer Science & Business Media, 2013.
 Note:
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 No timetable has been prepared for this course
 The course is a part of the following study plans: