Runge Kutta Methods for Differential-Algebraic Equations (DAEs)

This programme is focussed on the application of Implicit Runge-Kutta  methods for the DAEs arising from the spatial discretization of some evolution equations. Although, a good amount of literature is devoted to the analysis of IRK methods for the system of ODEs resulting from the finite element or finite difference discretization of time dependent PDEs, but there is hardly any result pertaining to the present programme. Therefore, an attempt has been made in the Thesis of Dr. Manickam to analyze and discuss higher order IRK schemes (ref. [28], [36] in the list of publications).