Michael Hanke - KTH
‘Least-squares collocation for higher index differential algebraic equations’
Collocation methods are well-established methods for the solution of boundary value problems in ordinary differential equations and index-1 differential-algebraic equations (DAEs). Higher index DAEs are ill-posed in naturally given topologies. Therefore, classical collocation methods provide unreliable results or break down completely. However, least-squares collocation is known to be a regularization method. Classical least-squares collocation has a rather low order of convergence.
In the present talk we report on preliminary convergence results for a method combining least-squares collocation and projection onto spaces of piecewise polynomials.
Computational experiments indicate its excellent convergence properties.
Michael Hanke has been an associate professor at KTH since 1998. He received his Ph.D. in Mathematics from Humboldt University of Berlin and has lectured in a variety of universities throughout the world, including the Computing Center of the Academy of Sciences of the USSR (Russia), Johannes Kepler University (Austria), University of Zaragoza (Spain), and University of Pittsburgh (USA). He has also worked in industry as a Scientific Consultant for Comsol AB and UTRC in East Hartford, Connecticut, USA. Michael's scientific Interests include the development of computational methods in systems biology and neuroscience.