Summer Semester 2009/10
Summer Semester 2010/11
Summer Semester 2011/12
Numerical methods TS2B100003
Course content:
Approximation of some functions in unitary spaces. Numerical approximation of some algebraic and vector operators.
Numerical integration and differentiation.
Numerical methods for ordinary differential equations.
The finite difference method: formulation and properties for parabolic, elliptic, and hyperbolic problems. FDTD algorithm.
The finite element and boundary element methods.
The sparse matrices: properties and some methods of their processing.
Solvers for linear matrix equations: iterative, Krylov subspace methods, conjugate gradient method.
Clusters and grids platforms: formulation and properties of distributed algorithms, available tools.
Learning outcomes:
Students are able to:
(a) use some methods to solve BVP or IVP problem;
(b) use some mathematical and specialized software;
(c) asses reliability of numerical results;
(d) validate and interpret results of implemented algorithms.
(in Polish) Rodzaj przedmiotu
Course coordinators
Bibliography
a) basic references:
Kincaid D., Cheney W.: Analiza numeryczna. WNT, Warszawa, 2006.
Fortuna Z., Macukow B., Wasowski J.: Metody numeryczne. WNT, 2005.
Krupka J., Morawski R.Z., Opalski L.J.: Wstęp do metod numerycznych. Oficyna Wyd. Polit. Warszawskiej, 2004.
William H.P.: Numerical recipes: the art of scientific computing. Cambridge Univ. Press, 2007.
Baron B., Piątek Ł.: Metody numeryczne w C++ Builder. Helion, 2004.
b) supplementary references:
Jianming J.: The finite element method in electromagnetics. J.Wiley&Sons, 1993.
Butcher J.C.: Numerical methods for ordinary differential equations. J.Wiley&Sons, 2003.
Evans G., Blackledge J., Yardley P.: Numerical methods for PDE. Springer, 2000.
Mathews J.H., Fink K.D.: Numerical methods using MATLAB. Pearson, 2004.
Taflove A.: Computational electrodynamics: the FDTD method. Artech House, 1996.
Buyya R.: High performance cluster computing, vol. 1 & 2, Prentice Hall PTR, 1999.