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Numerical Methods for Partial Differential Equations (PDE)
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Numerical Methods for Partial Differential Equations (PDE)
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Academic year 2023/2024
- Teachers
- Andrea Mignone
Gianluigi Bodo - Degree course
- PhD in Physics
- Year
- 1st year, 2nd year, 3rd year
- Teaching period
- Second semester
- Type
- Basic
- Credits/Recognition
- 4
- Course disciplinary sector (SSD)
- FIS/02 - theoretical physics, mathematical models and methods
FIS/03 - physics of matter
FIS/05 - astronomy and astrophysics
MAT/08 - numerical analysis - Delivery
- Traditional
- Language
- Italian
- Attendance
- Obligatory
- Type of examination
- Practice test
- Prerequisites
- Knowledge of Linux-like environments (Mac / Ubuntu / Windows Subsystem for Linux) and acquaintance with at least one programming language (C / C++ / Fortran).
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Sommario del corso
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Course objectives
The course aims at teaching the basic discretization methods for the solution of partial differential equations (PDE).
During the lectures, we will cover fundamental aspects concerning the three main categories: elliptic PDE, parabolic PDE and hyperbolic PDE.
Website: http://personalpages.to.infn.it/~mignone/PDE/
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Program
- Classification and examples of partial differential equations (elliptic, parabolic, hyperbolic) and some some analytical solution;
- Finite difference methods;
- Elliptic equations (Laplace and Poisson Equations): Gauss-Seidel, Jacobi and SOR methods;
- Parabolic equations (heat eq.): explicit methods, Crank-Nicholson and ADI methods;
- Hyperbolic PDE: characteristic cuerves, advection equation, burger equation (shocks and rarefaction), linear system and nonlinear equations (with application to Euler eqns.). Godunov's method.
Teaching tools: employement of Linux or Linux-like system is highly recommended, acquaintance with C or C++ is mandatory
Suggested readings and bibliography
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Notes
Period
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Wednesday April 3, 14:00-16:00 [Aula Fubini]
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Monday April 8, 14:00-16:00 [Aula Fubini]
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Wednesday April 10, 14:00-16:00 [Aula Fubini]
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Monday April 15, 14:00-16:00 [Aula Verde]
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Wednesday April 17, 14:00-16:00 [Aula Fubini]
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Wednesday April 24, 14:00-16:00 [Aula Fubini]
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Monday April 29, 14:00-16:00 [Aula Fubini]
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Tuesday April 30, 14:00-16:00 [Aula Fubini]
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Further information
http://personalpages.to.infn.it/%7emignone/PDE/- Enroll
- Open
- Enrollment opening date
- 02/11/2022 at 00:00
- Enrollment closing date
- 15/09/2024 at 00:00
- Maximum number of students
- 20 (Once this number of students is reached, enrollment will no longer be permitted!)
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