• Italiano
  • English

Department of Mathematics and Applications
"Renato Caccioppoli"


Numerical Methods for Ordinary Differential Equations

Home > Exams > Numerical Methods for Ordinary Differential Equations

Numerical Methods for Ordinary Differential Equations

Credits

6

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/08 Numerical Analysis.

Examination method

Oral exam and assessment of a project related to the course topics.

Learning
objectives

The course is an introduction to the development and analysis of methods for the numerical approximation of ordinary differential equations. Its main objective is to provide the tools for: understanding the methods through the analysis of accuracy and stability; implementing them correctly; studying the behaviour of the numerical solution through appropriate experimentation; and discussing alternative algorithms and drawing critical conclusions.

Syllabus

One-step and multistep numerical methods for initial value problems. Convergence and stability. Local and global error analysis. Explicit and implicit methods. Numerical solution of stiff systems. Linear and nonlinear stability theory. Symplectic methods for Hamiltonian systems. Numerical methods for boundary value problems. Laboratory work: development of codes based on the methods studied and numerical simulation of real phenomena using both the implemented algorithms and codes from numerical libraries available in the literature.

Expected learning
outcomes

On completion of the course, students must demonstrate that they

  • understand and know the numerical tools for solving non-trivial problems in science and engineering involving ordinary differential equations, with particular reference to the theoretical aspects of the problem itself and of its numerical solution;
  • can apply the knowledge acquired by independently developing programs for ordinary differential equations, including through the use of libraries and/or software environments
  • can communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
  • can identify the most appropriate methods to analyse and solve a problem relating to the course topics and interpret the results correctly.

Learning outcomes
to be assessed

Ability to develop the project independently; clarity, correctness and completeness in the oral presentation of the course topics.