66723 - Numerical Analysis and Scientific Software

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