The Differential Equations and Numerical Analysis Group

In 2010 the former Differential Equations and Numerical Analysis groups merged to form the new DNA group. It is one of the most active groups in the department in terms of

  • number of Master and PhD students
  • amount of research funding
  • number of published scientific papers

Main research areas

Most of the research of the group relates to differential equations in one way or another, including

  • the study of analytical properties of solutions
  • construction and analysis of numerical methods
  • mathematical modeling and applications

In addition there is research in applied numerical analysis such as quadrature methods and splines.

Nonlinear partial differential equations and fractional differential equations

  • hyperbolic conservation laws
  • nonlinear wave equations
  • nonlinear diffusion equations
  • p and infinity Laplace equations
  • Hamilton–Jacobi–Bellman equations
  • Camassa–Holm equations
  • fractional convection diffusion equations

Numerical analysis

  • ordinary, partial, stochastic, and fractional differential equations
  • geometric integration
  • structure preserving methods
  • highly oscillatory problems
  • spectral methods
  • reduced basis methods
  • isogeometric analysis
  • adaptivity

Computational mechanics

  • free surface problems
  • fluid-structure interaction
  • multiscale modelling

Mathematical physics

  • completely integrable systems
  • equations of relativity and quantum mechanics

Stochastic analysis

  • signal processing
  • ocean waves
  • control theorymathematical finance

Applications

  • flow in porous media
  • offshore wind turbines
  • rigid body dynamics
  • ocean waves
  • synthetic aperture radar
  • electrical circuit simulations

A solution of a variational wave equation. Figure.