Differential Equations and Numerical Analysis (DNA) - Mathematical Sciences
Differential equations and numerical analysis (DNA)

The DNA group works in the following areas:
Partial differential equations can be used to model phenomena such as gas flow through a pipeline or in porous media, water waves over an ocean or stock prices. Since Isaac Newton's initial studies, this field has witnessed an enormous development, and today practically all laws of nature are expressed in terms of differential equations. Central questions include whether there exists a solution of the equation; whether it is unique; and whether it is stable with respect to initial or boundary data.
Numerical methods of differential equations approximate the solution of a differential equation in a way suitable for implementation on computers. Thanks to advances in the field of numerical methods the past few decades, we have gotten better weather forecasts, safer cars and air planes, and we can predict the impact of tsunamis before they hit the shore.
Optimization theory covers problems where the main interest lies in finding the smallest or largest possible values of a function, given certain conditions. Such problems appear in a large number of physical models (such as minimal energy or entropy principles); medical or geophysical measurements (such as parameter identification or inverse problems); and improvements in the performance of technical or other systems (such as shape optimization).
We also teach a number of courses and offer project and master theses in the above areas.
Contact
Seminars and conferences
Recent publications
Current projects
Joint Training on Numerical Modelling of Highly Flexible Structures for Industrial Applications is a European Training Network project funded by EU's Horizon 2020 programme. The project period is 2019–2023 and the contact at NTNU is Elena Celledoni.
Wave Phenomena and Stability – a Shocking Combination is funded through a FRIPRO Young Research Talent grant, featuring Katrin Grunert as the principal investigator.
The main goal of Waves and Nonlinear Phenomena (WaNP) is to analyze the interplay of singularities and nonlocal effects in the solutions of partial differential equations that model wave phenomena.
Funded by FRIPRO Toppforsk, 2015–2021.
Bachelor and master courses
- TMA4165 Differential Equations and Dynamical Systems
- TMA4180 Optimization I
- TMA4183 Optimization II
- TMA4195 Mathematical modelling
- TMA4205 Numerical Linear Algebra
- TMA4212 Numerical Solution of Differential Equations by Difference Methods
- TMA4215 Numerical Mathematics
- TMA4220 Numerical Solution of Partial Differential Equations Using Element Methods
- TMA4305 Partial Differential Equations
- TMA4320 Introduction to Scientific Computation