Partially supported by Progetto Nazionale di Ricerca MURST “Analisi numerica: metodi e software scientifico”. Copyright © IMACS. Published by Elsevier.       V. Comincioli, Analisi Numerica, McGraw-Hill, G. Monegato, Fondamenti di Calcolo Numerico, Levrotto & Bella, V. Comincioli, Analisi Numerica, McGraw-Hill, G. Monegato, Fondamenti di Calcolo Numerico, Levrotto & Bella, O.C. Zienkiewicz and R.L. Taylor.
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METODI NUMERICI PER EQUAZIONI DIFFERENZIALI ORDINARIE
Teaching methods Lectures and guided exercises in the laboratory. The goal of this first part of the course is to introduce the student to the computational issues of the solutions of ordinary differential equations ODEs and to give several tools for the numerical resolutions of these problems.
My e-mail for students My e-mail for staff Close. Consistency, stability and convergence. To acquire basic abilities to solve problems and exercises by using numerical techniques for linear algebra, approximation of functions, nonlinear equations, cominncioli differential equations and computation of integrals. Texts of previous written exams are advertised and discussed during the course.
Scheda insegnamento — Laurea Triennale in Matematica
Moreover, to acquire the ability to suitably choose those methods which best fit the analosi situations. Romberg’s methods and adaptive methods. Representation of real numbers and machine arithmetic. Existence and uniqueness of a solution for implicit R-K methods. Numerical solution of Linear Systems: Introduction on the Cauchy problems: Cokincioli nel sito solo nella sezione corrente. Bulirsch, Intrpduction to numerical analysis, Springer, – L. Nonlinear systems fixed point method, local and global convergence, Newton and quasi-Newton methods, method globalization, inexact method ; 10 hours.
The final exam consists in an oral test, dedicated to verify the knowledge of the methods explained during the course and to discuss the results obtained in the individual assigned exercise.
Stability analysis for Runge-Kutta methods: Numerical solution of linear systems. A brief introduction to ordinary differential equations ODEs cominvioli, existence and Uniqueness theorem.
Lectures, both of theoretical xomincioli and aimed to the solution of exercises, also including the design and the execution of related computer programs. Numerical derivation formulae Richardson’s estrapolation technique ; stability.
Boundary value problems BVPs. Testo molto ampio e ricco di esempi. Multistep methods linear, explicit, implicit, predictor corrector methods: In particular,some important concepts will be introduced as: Rounding errors and their propagation.
During the lessons the theoretical discussion is supported by exercises in I.
Classico testo di Analilsi Numerica, molto vasto. Numerical methods for ODEs: Teaching Mode Traditional lectures. Biblioteche Servizi online Webmail. Shootingcollocation and finite difference methods 5 hours Didactic methods Lectures on all the topics previously stated are scheduled.
Mention on multiple integration 15 hours. Interpolating formulae Newton-Cotes ; Polya’s convergence theorem; composite quadrature anzlisi and convergence: Laboratory; these simulations are based on the implementation of the methods studied in class; the analysis regarding efficiency and effectiveness will be performed.
Consistency and convergence of R-K metohds and order conditions. Per appuntamento da concordare con il docente. Piazzale Cominciolk, 1 – – Trieste, Italia – Tel. This discussion allows amalisi the level of knowledge and skills acquired by the students on the methods learned.
Search Course unit catalogue. Geometria 1, Informatica, Analisi 2. The knowledge provided by this course regards numerical solution of nonlinear systems, numerical methods for derivation and integration, methods for the solution of differential equation systems with initial and boundary conditions.
Via Machiavelli, 30 – Ferrara Guarda la mappa. Back to list of courses. Eigenvalues and eigenvectors computation. Variable step size control. Links to further information http: Assessment methods Oral discussion of the laboratory projects.