Module Description

Module: Numerical Treatment of Ordinary Differential Equations

Courses:

TitleTypeHrs/WeekPeriod
Numerical Treatment of Ordinary Differential EquationsLecture2Summer Semester
Numerical Treatment of Ordinary Differential EquationsRecitation Section (small)2Summer Semester

Module Responsibility:

Prof. Sabine Le Borne

Admission Requirements:

None

Recommended Previous Knowledge:

  • Mathematik I, II, III für Ingenieurstudierende (deutsch oder englisch) oder Analysis & Lineare Algebra I + II sowie Analysis III für Technomathematiker
  • Basic MATLAB knowledge

Educational Objectives:

Professional Competence

Theoretical Knowledge

Students are able to

  • list numerical methods for the solution of ordinary differential equations and explain their core ideas,
  • repeat convergence statements for the treated numerical methods (including the prerequisites tied to the underlying problem),
  • explain aspects regarding the practical execution of a method.
  • select the appropriate numerical method for concrete problems, implement the numerical algorithms efficiently and interpret the numerical results
Capabilities

Students are able to

  • implement (MATLAB), apply and compare numerical methods for the solution of ordinary differential equations,
  • to justify the convergence behaviour of numerical methods with respect to the posed problem and selected algorithm,
  • for a given problem, develop a suitable solution approach, if necessary by the composition of several algorithms, to execute this approach and to critically evaluate the results.


Personal Competence

Social Competence

Students are able to

  • work together in heterogeneously composed teams (i.e., teams from different study programs and background knowledge), explain theoretical foundations and support each other with practical aspects regarding the implementation of algorithms.
Autonomy

Students are capable

  • to assess whether the supporting theoretical and practical excercises are better solved individually or in a team,
  • to assess their individual progress and, if necessary, to ask questions and seek help.

ECTS-Credit Points Module:

6 ECTS

Examination:

Written exam

Workload in Hours:

Independent Study Time: 124, Study Time in Lecture: 56


Course: Numerical Treatment of Ordinary Differential Equations

Lecturer:

Christian Seifert

Language:

German & English

Period:

Summer Semester

Content:

Numerical methods for Initial Value Problems

  • single step methods
  • multistep methods
  • stiff problems
  • differential algebraic equations (DAE) of index 1

Numerical methods for Boundary Value Problems

  • multiple shooting method
  • difference methods
  • variational methods

Literature:

  • E. Hairer, S. Noersett, G. Wanner: Solving Ordinary Differential Equations I: Nonstiff Problems
  • E. Hairer, G. Wanner: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems