Lecturer(s)


Brzezina Miroslav, doc. RNDr. CSc.

Course content

Systems of ordinary differential equations (ODR). Especially linear ones with constant coefficients. Own numbers and matrix vectors. Stability of the solution. Numerical solution of Cauchy tasks for nth order differential equations and firstorder systems in normal form (single and multistep methods). Numerical solution of boundary problems for ordinary 2nd order differential equations, shooting method, boundary conditions method, network method. Interpolation and approximation. The smallest square method. Quadrature formulas. Numerical solution of systems of linear equations. Partial Differential Equations (PDR). Marginal and mixed tasks. Network Method. Mathematical basics of the finite element method. Triangulation of the area. Basic finite elements

Learning activities and teaching methods

Lecture

Learning outcomes

Systems of ordinary differential equations (ODR). Especially linear ones with constant coefficients. Own numbers and matrix vectors. Stability of the solution. Numerical solution of Cauchy tasks for nth order differential equations and firstorder systems in normal form (single and multistep methods). Numerical solution of boundary problems for ordinary 2nd order differential equations, shooting method, boundary conditions method, network method. Interpolation and approximation. The smallest square method. Quadrature formulas. Numerical solution of systems of linear equations. Partial Differential Equations (PDR). Marginal and mixed tasks. Network Method. Mathematical basics of the finite element method. Triangulation of the area. Basic finite elements

Prerequisites

unspecified

Assessment methods and criteria

Combined examination

Recommended literature


Braess, D. Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics Cambridge University Press. Cambridge, 2001.

Brzezina M., Veselý J. Obyčejné (lineární) diferenciální rovnice a jejich systémy. Liberec, 2012. ISBN 9788073729097.

Stoer J., Bulirsch R.:. Introduction to Numerical Analysis. Springer. ISBN 038795452X.
