Introduce to the study and implementation of more advanced numerical approximation techniques, in particular related to approximate solution of ordinary differential equations, and to a further advanced topic to be chosen between the optimization and the fundamentals of approximation of partial differential equations.
Curriculum
teacher profile teaching materials
Finite difference approximation for ordinary differential equations: Euler's method. Consistency, stability, absolute stability. Second order Runge-Kutta methods.
Single step implicit methods: backward Euler and Crank-Nicolson methods. Convergence of single step methods. Multi-step methods: general structure, complexity, absolute stability. Stability and consistency of multi-step methods. Adams methods, BDF methods, Predictor-Corrector methods. (Reference: Chapter 7 of curse notes "Appunti del corso di Analisi Numerica")
Partial Differential Equations
Finite difference approximation for partial differential equations. Semi-discrete approximations and convergence. The Lax-Richtmeyer theorem. Transport equation: the method of characteristics. The "Upwind" (semi-discrete and fully-discrete) scheme, consistency and stability. Heat equation: Fourier approximation. Finite difference scheme, consistency and stability. Poisson equation: Fourier approximation. Finite difference scheme, convergence. (Reference: notes by R. LeVeque, "Finite Difference methods for differential equations", selected chapters 1, 2, 3, 12, 13)
Roberto Ferretti, "Esercizi d'esame di Analisi Numerica", in pdf at http://www.mat.uniroma3.it/users/ferretti/Esercizi.pdf
Lecture slides in pdf at http://www.mat.uniroma3.it/users/ferretti/bacheca.html
Additional notes given by the teacher
Mutuazione: 20410420 AN420 - ANALISI NUMERICA 2 in Scienze Computazionali LM-40 CACACE SIMONE
Programme
Ordinary Differential EquationsFinite difference approximation for ordinary differential equations: Euler's method. Consistency, stability, absolute stability. Second order Runge-Kutta methods.
Single step implicit methods: backward Euler and Crank-Nicolson methods. Convergence of single step methods. Multi-step methods: general structure, complexity, absolute stability. Stability and consistency of multi-step methods. Adams methods, BDF methods, Predictor-Corrector methods. (Reference: Chapter 7 of curse notes "Appunti del corso di Analisi Numerica")
Partial Differential Equations
Finite difference approximation for partial differential equations. Semi-discrete approximations and convergence. The Lax-Richtmeyer theorem. Transport equation: the method of characteristics. The "Upwind" (semi-discrete and fully-discrete) scheme, consistency and stability. Heat equation: Fourier approximation. Finite difference scheme, consistency and stability. Poisson equation: Fourier approximation. Finite difference scheme, convergence. (Reference: notes by R. LeVeque, "Finite Difference methods for differential equations", selected chapters 1, 2, 3, 12, 13)
Core Documentation
Roberto Ferretti, "Appunti del corso di Analisi Numerica", in pdf at http://www.mat.uniroma3.it/users/ferretti/corso.pdfRoberto Ferretti, "Esercizi d'esame di Analisi Numerica", in pdf at http://www.mat.uniroma3.it/users/ferretti/Esercizi.pdf
Lecture slides in pdf at http://www.mat.uniroma3.it/users/ferretti/bacheca.html
Additional notes given by the teacher
Type of delivery of the course
frontal teaching courseType of evaluation
theoretical oral test and evaluation of a matlab project teacher profile teaching materials
Finite difference approximation for ordinary differential equations: Euler's method. Consistency, stability, absolute stability. Second order Runge-Kutta methods.
Single step implicit methods: backward Euler and Crank-Nicolson methods. Convergence of single step methods. Multi-step methods: general structure, complexity, absolute stability. Stability and consistency of multi-step methods. Adams methods, BDF methods, Predictor-Corrector methods. (Reference: Chapter 7 of curse notes "Appunti del corso di Analisi Numerica")
Partial Differential Equations
Finite difference approximation for partial differential equations. Semi-discrete approximations and convergence. The Lax-Richtmeyer theorem. Transport equation: the method of characteristics. The "Upwind" (semi-discrete and fully-discrete) scheme, consistency and stability. Heat equation: Fourier approximation. Finite difference scheme, consistency and stability. Poisson equation: Fourier approximation. Finite difference scheme, convergence. (Reference: notes by R. LeVeque, "Finite Difference methods for differential equations", selected chapters 1, 2, 3, 12, 13)
Roberto Ferretti, "Esercizi d'esame di Analisi Numerica", in pdf at http://www.mat.uniroma3.it/users/ferretti/Esercizi.pdf
Lecture slides in pdf at http://www.mat.uniroma3.it/users/ferretti/bacheca.html
Additional notes given by the teacher
Mutuazione: 20410420 AN420 - ANALISI NUMERICA 2 in Scienze Computazionali LM-40 CACACE SIMONE
Programme
Ordinary Differential EquationsFinite difference approximation for ordinary differential equations: Euler's method. Consistency, stability, absolute stability. Second order Runge-Kutta methods.
Single step implicit methods: backward Euler and Crank-Nicolson methods. Convergence of single step methods. Multi-step methods: general structure, complexity, absolute stability. Stability and consistency of multi-step methods. Adams methods, BDF methods, Predictor-Corrector methods. (Reference: Chapter 7 of curse notes "Appunti del corso di Analisi Numerica")
Partial Differential Equations
Finite difference approximation for partial differential equations. Semi-discrete approximations and convergence. The Lax-Richtmeyer theorem. Transport equation: the method of characteristics. The "Upwind" (semi-discrete and fully-discrete) scheme, consistency and stability. Heat equation: Fourier approximation. Finite difference scheme, consistency and stability. Poisson equation: Fourier approximation. Finite difference scheme, convergence. (Reference: notes by R. LeVeque, "Finite Difference methods for differential equations", selected chapters 1, 2, 3, 12, 13)
Core Documentation
Roberto Ferretti, "Appunti del corso di Analisi Numerica", in pdf at http://www.mat.uniroma3.it/users/ferretti/corso.pdfRoberto Ferretti, "Esercizi d'esame di Analisi Numerica", in pdf at http://www.mat.uniroma3.it/users/ferretti/Esercizi.pdf
Lecture slides in pdf at http://www.mat.uniroma3.it/users/ferretti/bacheca.html
Additional notes given by the teacher
Type of delivery of the course
frontal teaching courseType of evaluation
theoretical oral test and evaluation of a matlab project