Software by Carlo Zambaldo ([email protected]) This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Raccolta di alcune funzioni utili durante il corso di Calcolo Numerico

• insiemeF
• condizioni (requires controlla) finds propreties of Matrices and shows methods to solve the linear system "Ax=b".
• Wilkinson estimates the maximum value of the perturbation expected on a given matrix
• controlla

• condizioniF
• metodocorde
• metodosecanti
• ptofis_sistemi
• molteplicity computes the molteplicity of the zero of a function

• CGL (chebyshev Gauss Lobatto) computes CGL knodes given the number of knodes-1 required and the interval [a,b]
• Lebesgue (requires funzione_caratteristica_lagrange) draws Lagrange polynomials and prints out the Lebesgue constant
• funzione_caratteristica_lagrange
• interp_trigo.m outputs the trigonometric interpolator as a function handle

• grado_di_esattezza computes the degree of accuracy of a numerical formula (for the integration)
• stability_region, stability_region_contour plots the stability region of a particular numerical method (notice: the stability function is required!)
• leap_frog implements the Leap-Frog method
• runge_kutta solves the given Cauchy Problem, given a particular Butcher tableau.

• diffusione_trasporto_reazione, diffusione_trasporto_reazione_DN, diffusione_trasporto_reazione_ND, diffusione_trasporto_reazione_NN these scripts solve a diffusion-transport-reaction problem on the interval [a,b] (the _XY after "diffusione_trasporto_reazione" stands for the type of boundary conditions (X for point a and Y for point B): N = Newmann, D = Dirichlet, if not present is DD). Please notice: sometimes the program suggests better viscosity to reduce numerical oscillations.
• pechlet evaluates local Péclet number

• deriva outputs the derivative of the given function as a function handle
• integra outputs the integral of the given function as a function handle (notice: no constant added [c=0]!)
• jacobiana

• stimaalgebrica_p estimates C and p in: err <= C * h^p
• stimaerr
• plot_soluzione quickly plots the solution obtained with a numerical method (i.e. diffusione_trasporto_reazione)
• tridiag outputs a tridiagonal matrix
• pentadiag outputs a pentadiagonal matrix
• poly2func

Please notice: the function sym2fun was written by Marty Lawson (more info inside the script)

Copyright 2021 Carlo Zambaldo

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