On the randomized solution of initial value problems

Abstract: We study the randomized solution of initial value problems for systems of ordinary differential equations Recently Heinrich and Milla (2008)  presented an order optimal randomized algorithm solving this problem for -smooth input data (i.e. : the -th derivatives of satisfy a -Hölder condition). This algorithm uses function values and values of derivatives of . In this paper we present an order optimal randomized algorithm for the class of -smooth functions that uses only values of . For this purpose we show how to obtain an order optimal randomized algorithm from an order (sub)optimal deterministic one. [Copyright &y& Elsevier]