Numerikus módszerek 2.

(Horváth Róbert)
    FINITE DIFFERENCE METHODS
  1. Numerical solution of one-dimensional parabolic problems with explicit methods. [MORTON, pages 7-21]
  2. Numerical solution of one-dimensional parabolic problems with implicit and - methods, maximum principle [MORTON, pages 22-24, 26-38]
  3. Numerical solution of one-dimensional hyperbolic equations, CFL-condition, analysis of the upwind scheme [MORTON, pages 86-100]
  4. Lax-Wendroff and the leap-frog schemes and their analysis [MORTON, pages 100- 110, 123-128].
  5. Consistency, convergence and stability, Lax equivalence theorem [MORTON, pages 151-169].
  6. Finite difference solution of the two-dimensional Poisson equation [MORTON, pages 194-203].
  7. Multigrid method [BORZI, pages 9-22].

    FINITE ELEMENT METHODS
  8. Introduction of the finite element method (FEM) on a one-dimensional problem. FEM for the Poisson equation [JOHNSON, pages 14-33].
  9. Some special Hilbert spaces, geometrical interpretation, Neumann boundary conditions [JOHNSON, pages 33-43].
  10. Abstract formulation of FEM for elliptic problems [JOHNSON, pages 50-67].
  11. Some finite element spaces [JOHNSON, pages 67-84].
  12. Error estimates for elliptic problems [JOHNSON, pages 84-92].
A rövidítések az alábbi könyveket jelentik: [MORTON]: Morton, Mayers, Numerical solutions of partial differential equations, Cambridge University Press, 2005, [BORZI]: Alfio Borzi, Introduction to multigrid methods, Institut für Mathematik und Wissenschaftliches Rechnen, [JOHNSON]: Johnson, Numerical solutions of PDEs by the finite element methods.