Educational guide 2008_09 Escola Tècnica Superior d`Enginyeria Química

Contents

Topic	Sub-topic
0. Discrete representation of real numbers and numerical error. The corresponding exercises will also serve as an introduction to programing numerical methods, so do not miss these first classes!	significant digits, relative accuracy, error propagation, interval arithmetics. Not-so-equivalent formulas and tricks in sample cases.
1. Solution of algebraic equations f(x)=0.	General methods suitable for non-linear equations: successive substitution, bisection, Newton-Raphson (1 and 2 unknowns). Warnings on multiple roots and multiplicity of each root. Methods for linear systems might or might not be discussed.
2. Evaluation of integrals (very brief mention)	rectangles, trapeze and Simpson rules.
3. Solution of Ordinary Differential Equations (mostly initial value problems).	Euler (forward and backward) and Runge-Kutta methods. Stability of explicit methods. Higher-order equations and systems of equations (up to 2). Stiffness. Backwards differentiation formulas. Two-point problem: shooting mehtod.
4. Solution of Partial Differential Equations (mostly initial value problems)	Flux conservation and wave equation: Forward Time Centered Space algorithm. Von Neumann stability analysis. Leap-frog algorithm. Courant condition. Diffusion equation: FTCS algorithm and associated Courant condition (in arbitrary dimensions). Crank-Nicolson algorithm. Bilaplacian operator. Etc. (depending on time left for the course). Relaxation and equilibrium methods for boundary value problems.