Educational guide Escola Tècnica Superior d`Enginyeria Química |
english |
Enginyeria Ambiental (2006) |
Subjects |
MÈTODES NUMÈRICS |
Contents |
IDENTIFYING DATA | 2008_09 |
Subject | MÈTODES NUMÈRICS | Code | 205141224 | |||||
Study programme |
|
Cycle | 2nd | |||||
Descriptors | Credits | Type | Year | Period | ||||
3 | Optional | Only annual |
Competences | Learning aims | Contents |
Planning | Methodologies | Personalized attention |
Assessment | Sources of information | Recommendations |
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. |