Differential Equations and Numerical Analysis Group

In 2010 the former Differential Equations and Numerical Analysis groups merged to form the new DNA group (DNA=Differential equations and Numerical Analysis). It is one of the most active groups in the department in terms of the number of master and PhD students, the amount of research funding, and the number of published scientific papers.

Most of the research of the group relates to differential equations in one way or another, e.g. the study of analytical properties of solutions, construction and analysis of numerical methods, and mathematical modeling and applications. In addition there is research in numerical analysis with other applications such as quadrature methods and splines. The main areas of research are:

  • 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 theory, mathematical 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

A solution of a variational wave equation