Article ID Journal Published Year Pages File Type
4608809 Journal of Complexity 2011 12 Pages PDF
Abstract

We study the randomized solution of initial value problems for systems of ordinary differential equations y′(x)=f(x,y(x)),x∈[a,b],y(a)=y0∈Rd. Recently Heinrich and Milla (2008) [4] presented an order optimal randomized algorithm solving this problem for γγ-smooth input data (i.e. γ=r+ργ=r+ρ: the rr-th derivatives of ff satisfy a ρρ-Hölder condition). This algorithm uses function values and values of derivatives of ff. In this paper we present an order optimal randomized algorithm for the class of γγ-smooth functions that uses only values of ff. For this purpose we show how to obtain an order optimal randomized algorithm from an order (sub)optimal deterministic one.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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