Numerical Methods for Chemical Engineering D-CAHB 2012

• 19.09.2012: introduction; modeling, discretisation and numerical solution on an example; propagation of the round-offerrors in an iteration; quadrature; algebraic and exponential convergence, Landau O-notation; trapezoidal, Simpson, Gauss, Clenshaw-Curtis; composite quadrature; Theorem on error

• 26.09.2012: examples of quadrature (slides); adaptivity; ODEs, reduction tricks with examples; existence and unicity result; examples; explicit Euler method

• 02.10.2012: one-step methods (eE, iE, iMP, iTR); Stoermer-Verlet; velocity Verlet and leapfrog; structrure preservation; convergence order

• 03.10.2012: splitting methods, time-dependent Schroedinger equation, linear IVPs and linearisation, Runge-Kutta with examples (eTR, eMP), Butscher tableau

• 10.10.2012: general Runge-Kutta, adaptive time-stepping, ode45; stability and stiffness

• 17.10.2012: stiff problems and appropriate solvers; iterative methods, fix point iterations, Newton method

• 27.10.2012: Newton method, simplified Newton method, Broyden Quasi-Newton method; method of steepest descent, preconditioned conjugate gradient; started SVD

• 31.10.2012: singular value decomposition and PCA; orthogonality; QR-decomposition

• 07.11.2012: linear and non-linear least squares