Numerical Metods for Quantum Technologies

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Department of Mathematics

Synopsis:

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, finite-difference and finite-volume methods for elliptic, parabolic and first-order hyperbolic partial differential equations. Some methods based on stochastic or particle approach are discussed as well.

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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

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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.

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No time-table has been prepared for this course

The course is a part of the following study plans: