## Numerical Analysis Course LM A.A. 2013/2014

II ciclo, CFU 6

### TIME SCHEDULING:

• Teachers:
• Course contents
• Exams
• Bibliography
• Teaching Notes

### Course contents

Learning outcomes:
The course covers the basic techniques for iterative methods for solving linear system of equations, the solution of problems modeled by Ordinary Differential Equations (ODE) e BVP (Boundary Value problems). Next, the course presents numerical methods for the solution of problems modeled by Partial Differential Equations (PDE). Part A: A first course in Numerical Analysis. Covers the basic techniques for iterative methods for solving linear system of equations, the solution of problems modeled by Ordinary Differential Equations (ODE) e BVP (Boundary Value problems). The course discusses their analysis, applications, and computation of the solution by numerical methods. Part B: This second part of the course presents numerical methods for the solution of problems modeled by Partial Differential Equations (PDE). The course discusses their analysis, applications, and computation of the solution (by first discretizing the equation, bringing it into a finite-dimensional subspace by a finite element method, or a finite difference method , and finally reducing the problem to the solution of an algebraic equations)
Course contents:

• PART I Numerical Methods for ODE
Quadrature: basic quadrature rules, Newton Cotes rules. Ordinary Differential Equations: one-step methods: euler and runge-kutta methods,multi-step methods: Predictor-corrector scheme,numerical solution of stiff problems Boundary value Problems
• PART II: Numerical Methods for PDE
Solving Linear Systems. Iterative methods: Gauss-Seidel, SOR, Steepest Descent, Conjugate Gradient Numerical Differentiation Partial Differential Equations: classification, Numerical methods: finite difference schemes, finite element schemes for parabolic-type and elliptic-type problems. Introduction to the COMSOL computing environment . Miscellaneous problems and applications

• ### Exams

Assessment methods:
Projects where the numerical methods are used in specific applications will be assigned throughout the course. Oral exam and final discussion about the projects.
Final Project Report

### Bibliography

R.J.LeVeque, Finite Difference Methods for ODEs and PDEs, Steady State and Time Dependent Problems. SIAM, Philadelphia, 2007
A. Quarteroni, Modellistica Numerica per problemi Differenziali, Springer, Ed. 4a, 2008.
G. Monegato, Fondamenti di Calcolo Numerico, CLUT, 1998.
Kincaid Cheney, Numerical Analysis , Brooks and Cole.,1991

English