Course content

Initial- and boundary-value problems for ordinary differential equations using shooting techniques and difference methods. Numerical solution of partial differential equations using difference methods. Both explicit and implicit schemes are used; mostly one-dimensional transient problems. Use of Fourier stability analysis. Stationary problems in two dimensions. The examples and problems are taken mainly from the following fields: Heat transfer, dynamics, elasticity and fluid mechanics. Matlab is used throughout the course; both in the examples and for solving exercises. A short introduction to Fortran90 is given at the end of the course.

Learning outcome

This course will provide an introduction to the use of classical numerical methods for ordinary and partial differential equations applied to examples from the first 2-3 years of the study, primarily for the academic programs MTPROD, MTING and MTBYGG. The subject is mandatory for the program Industrial Mechanics.

The following abbreviations are used below :
ODE : Ordinary differential equations
PDE : Partial differential equations

Knowledge:
The candidate will learn about:
- When it is necessary to use numerical methods.
- Advantages /disadvantages of different computer languages.
- The difference between linear and nonlinear equations.
- Advantages /disadvantages of different classical methods for the
solution of ODE.
- The difference between parabolic, elliptical and hyperbolic PDE

Skills:
The candidate will be able to:
- Write a higher order ODE as a system of 1. order equations.
- Program this system using different schemes in Matlab and/or Fortran.
- Using ready-made programs for the solution of ODE.
- Discretize and programming ODE (in Matlab and/or Fortran).
- Linearize the discretized system if neccessary.
- Discretize the three main types of PDE, and programming of the resulting systems.
- Examine the stability of the PDE.

General competence:
The candidate will be able to:
- Use Matlab and programming for furher use in the study.
- Have the basic foundation for the use of more advanced numerical methods.

Learning methods and activities

Lectures and problem-solving supplemented with programming in Matlab, python and Fortran90, mainly Matlab. If there is a re-sit examination, the examination form may be changed from written to oral.

Compulsory assignments

• Exercises

Recommended previous knowledge

Subject TDT4105 Information Technology, Introduction. Subject TMA4130, Mathematical Subjects, Advanced Course, is recommended, but not required.

Course materials

Compendium. Notes with introduction to Matlab. Collection of problems with solutions given in earlier examinations.

Credit reductions