Numerical Methods for Chemical Engineering D-CHAB 2013

• 23.10.2013: introduction, 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, composite quadrature; Theorem on error; examples of quadrature; adaptivity

• 30.10.2013: first order ordinary differential quations: definitions and examples; explicit Euler, implicit Euler, implicit midpoint rule, implicit trapezoidal rule; convergence order; stability; conservation laws; started discussion on Stoermer-Verlet method

• 06.11.2013: Stoermer-Verlet as two-step method, as one-step method on staggered grid and as velocity-Verlet; splitting methods with important examples from mechanics; Runge-Kutta methods with examples; adaptivity in time and ode45

• 13.11.2013: overview of the methods; stability; stiff problems; started numerical methods for algebraic equations: iterative scheme, speed of convergence, stoping criteria

• 20.11.2013: case studies, NO lecture on numerical methods

• 27.11.2013: fix point iterations, Newton method, simplified Newton method

• 04.12.2013: stoping Newton-iteration, Broyden Quasi-Newton method; orthogonality; LU- and QR-decomposition; singular value decomposition and PCA

• 11.12.2013: singular value decomposition and condition of a matrix; linear least squares problems: normal equation and how to avoid its use, solution via QR-decomposition and via SVD; linear least squares problems with linear constraints; non-linear least square problems: Newton method and Gauss-Newton, Levenberg-Marquardt method

• 18.12.2013: iterative methods for large sparse systems of linear equations