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, but also introduction to the finite element method if time allows. 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 primarily from the following fields: Heat transfer, dynamics, elasticity and fluid mechanics. The principle teaching resource for the course will be a digital compendium which integrates theory, examples and python-programs.

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 equation, PDE : Partial differential equation, IVP/BVP: initial and boundary value problem. Knowledge: The candidate will learn about: - When it is necessary to use numerical methods. - Advantages /disadvantages of different classical methods for the solution of ODEs IVPs and BVPs. - Linearization of non-linear algebraic equations/systems resulting from the discretization of those problems. - The difference between parabolic, elliptical and hyperbolic PDEs. - Basic finite difference schemes for each one of these PDE classes. - Accuracy, consistency and stability of numerical schemes for ODEs and PDEs. Skills: The candidate will be able to: - Identify initial and boundary value problems for ODEs, choose a discretization strategy, implement the resulting ODE solver using python as a programing language. In that context, the student will learn how to deal with ODE systems or how to reduce higher order ODEs to a system of first order ODEs, as well as how to linearize the discrete version of the problem when necessary. - Discretise the three main types of PDEs using finite difference methods and program the resulting numerical scheme. - Examine the stability of the derived numerical schemes for different PDE classes.
- Examine the accuracy of numerical methoods for ODEs and PDEs.
General competence: The candidate will have fundamental competence in: - Programming (python) to be used later in the studies. - Numerical methods for engineering applications as a foundation for more advanced numerical methods at later stages in the studies.

Learning methods and activities

Lectures and problem-solving supplemented with programming primarily in python. The lectures and exercises will be given in English if students not fluent in Norwegian are taking th course or if there are other practical reasons for doing so. If the lectures are given in English, the exam will be typed in English only. Students are free to to hand in their answers in Norwegian or English. Most of the teaching material is written in English.

Compulsory assignments

• Exercises

Recommended previous knowledge

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

Course materials

Digital compendium, downloadable example code, tutorials etc.

Credit reductions