# 35433 - Numerical Methods

### Course Unit Page

• Teacher Fabiana Zama

• Credits 6

• SSD MAT/08

• Teaching Mode Traditional lectures

• Language English

• Campus of Bologna

• Degree Programme Second cycle degree programme (LM) in Mathematics (cod. 5827)

Also valid for Second cycle degree programme (LM) in Mathematics (cod. 8208)

• Course Timetable from Sep 21, 2021 to Dec 16, 2021

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

## Learning outcomes

At the end of the course, students know basic numerical methods for evolutive ordinary and partial differential problems, together with their main theoretical and computational properties. In particular, students are able to analyze the properties of numerical methods; constructively examine corresponding computational results; advance their scientific computing education in higher level courses; employ the acquired numerical skills in a variety of application areas.

## Course contents

• Numerical solution of non-linear systems
• Gaussian quadrature formulas
• Numerical solution of Ordinary Differential Equations
• Initial value problems
• Onestep-multistep methods
• Convergence, stability
• Boundary value problems
• Shooting Method
• Finite difference method
• Galerkin’s Method
• Time dependent Partial Differential Equations: Method of Lines

Prerequisites

- Matlab programming

- Floating point arithmetic.
- Numerical methods for the solution of linear systems;

- Numerical methods for the solution of nonlinear equations.
- Data approximation: polynomial and piecewise polynomial functions; interpolation and least-squares approximation.
- Numerical integration: Newton-Cotes quadrature formulas.

## Readings/Bibliography

• Course Lecture notes
• U. Ascher and L. Petzold. Computer methods for ordinary differential equations and differential-algebraic equations. SIAM, 1998.
• D.F. Griffths and D.J. Higham. Numerical Methods for Ordinary Differential Equations: Initial Value Problems. Springer, 2010.
• Randal J. LeVeque. Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM, 2007.
• Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri. Numerical Mathematics (Texts in Applied Mathematics). Springer-Verlag, Berlin, Heidelberg, 2006.
• H.B.Keller. Numerical Methods for Two-Point Boundary Value Problems. Dover Ed., 2018.

## Teaching methods

Classroom lectures and computer laboratory

## Assessment methods

• Laboratory Project
• Written test and oral discussion.

## Teaching tools

e-learning platform: Virtuale

## Office hours

See the website of Fabiana Zama