The Matlab environment and programming language. Polynomial and spline interpolation. Newton-Cotes, composite and adaptive quadrature rules. Numerical methods for the Cauchy problem.
-L. Brugnano, C. Magherini, A. Sestini, Calcolo Numerico, Master, Università e Professioni, Terza Edizione, Firenze 2014.
-A. Quarteroni, R. Sacco, F. Saleri, Matematica numerica, Springer, –Verlag Milano, 2000.
-V. Comincioli, Analisi Numerica. Metodi, modelli e applicazioni, Mc Graw Hill, Milano, 1990.
Learning Objectives
Knowledges: basic numerical methods for function approximation and for quadrature; fundamental one-step numerical schemes for the numerical solution of the Cauchy problem.
Expertise: Matlab programming, organization of numerical experiments and presentation of obtained results.
Prerequisites
Numerical Calculus
Teaching Methods
5 hours a week, 2 in classroom (frontal teaching) and 3 in computer lab (implementation and testing of the introduced methods)
Type of Assessment
The exam consists in an oral interrogation and in discussing a student's work (Matlab implementation of the introduced numerical schemes and presentation of results from numerical experiments)
Course program
Matlab: work environment and programming language. Polynomial and spline interpolation. Newton-Cotes and composite quadrature rules, study of their conditioning and of their error expression. Adaptive quadrature rules. Numerical methods for the Cauchy problem: consistency, stability, convergence, absolute stability. Explicit and implicit Euler methods, Crank-Nicholson scheme. Runge-Kutta methods: generalities, and derivation of second order explicit schemes. Runge-Kutta-Fehlberg schemes.