First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS
SCP3051019, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 7.0
Type of assessment Mark
Course unit English denomination NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS
Website of the academic structure http://matematica.scienze.unipd.it/2019/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge MARIO PUTTI MAT/08
Other lecturers STEFANO DE MARCHI MAT/08

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/08 Numerical Analysis 3.0
Core courses MAT/08 Numerical Analysis 4.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Laboratory 1.0 16 9.0 No turn
Lecture 6.0 48 102.0 No turn

Calendar
Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
7 Metodi Numerici per le Equazioni Differenziali - a.a. 2019/2020 01/10/2019 30/09/2020 PUTTI MARIO (Presidente)
DE MARCHI STEFANO (Membro Effettivo)
CAMPI CRISTINA (Supplente)
MARCUZZI FABIO (Supplente)
SOMMARIVA ALVISE (Supplente)

Syllabus
Prerequisites: Mathematical Analysis 1 and 2, with elements of Differential Equations and functional analysis. Numerical Analysis and linear algebra. The lab projects require some knowledge of Matlab programming.
Target skills and knowledge: The course deals with methods of scientific computing and numerical analysis for the solution of partial differential equations. We will address both application and implementation issues as well as theoretical results. The course will also address many of the instruments that are necessary to complete the numerical solution of a PDE, such as solution of ODEs, solution of large sparse linear systems of equations. The lab projects will provide the students with the opportunity to challenge themselves in practical implementation issues.
Examination methods: Oral examination with discussion on the lab projects.
Assessment criteria: 30% lab projects
70% oral discussion
Course unit contents: Ordinary differential equations. Generalities, existence and uniqueness. Discrete methods: one step-methods, Runge-Kutta methods. stability and convergemce. Multi-step methods. Stiff problems, linear and nonlinear stability, implementation.
Partial differential equations: characterization with description of most important model problems. FEM methods for elliptic equations: variational formulation, Hilbert spaces; boundary conditions (Dirichlet, Neumann, Cauchy). Abstract FEM formulation: energy norm, discretization, error estimates, regularity of the solution. Parabolic equations: spatio-temporal discretizations. Error and stability estimates for Euler and Crank-Nicolson methods. Applications to nonlinear problems.
Planned learning activities and teaching methods: Classroom and computer laboratory. The theoretical notions will be discussed on the blackboard. The implementation issues and usage of the different algorithms will be discussed in the computer lab.
Additional notes about suggested reading: Lecture notes written by the teacher will be available for most of the material.
Textbooks (and optional supplementary readings)
  • Quarteroni, Alfio, Numerical Models for Differential Problems. Springer Milan: --, 2014. Cerca nel catalogo
  • Quarteroni, Alfio; Valli, Alberto, Numerical approximation of partial differential equationsAlfio Quarteroni, Alberto Valli. Heidelberg: Springer, --. Cerca nel catalogo
  • Hairer, Ernst; Wanner, Gerhard, <<2: >>Stiff and differential-algebraic problemsE. Hairer, G. Wanner. Berlin [etc.]: Springer, --. Cerca nel catalogo
  • Hairer, Ernst; Wanner, Gerhard, <<1: >>Nonstiff problemsE. Hairer, S. P. Norsett, G. Wanner. Berlin \etc.!: Springer, --. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Questioning
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • Matlab