Analysis of fractional-rational methods for stiff ODE systems

Abstract

The purpose of this work is to investigate the different class of fractional rational methods.The consistency, local error and convergence is analysed with a special focus on an order reduction for a stiff ODEs.The starting point is the construction of the new multi-step method in a fractional rational form involving the Adams-Basforth scheme. Because of the occurrence of parasitic roots we replaced it by the general linear multi-step method. However this solution lead us to the order reduction for a very stiff problem. The second part of thesis deal with the exponential integrators which does not cause an order reduction. The replacement of the exponential function in method by a sub-diagonal Pade approximation lead us to well know method for which the local error and convergence were nor investigated earlier. The results and proof is presented in thesis.In every case we present a numerical test which were done in computer algebra system Maple.