Title : B-SERIES FOR THE ANALYSIS OF NUMERICAL METHODS

Abstract :

The accuracy of many numerical methods can be analysed in terms of Taylor series. In the special case of solutions to autonomous differential equations, and approximate solutions found from numerical methods, the series can be written in terms of elementary differentials. These series expansions are referred to as B-series. One of the central ideas is the composition group and extensions and generalizations of this group. It will be shown how important questions related to the accuracy of numerical methods for differential equations can be expressed in terms of B-series. Intricate but practical numerical methods can be derived using these seemingly abstract ideas.