We study computabilty of the abstract linear Cauchy problem ::: ::: du(t)/dt=Au(t), t>0, u(0)=x∈X ::: ::: where A is a linear operator on a Banach space X. We give necessary and sufficient conditions for A such that the operator K:x↦ u is computable. We consider continuous operators and more generally closed operators A. For studying computability we use the representation approach to Computable Analysis (TTE) [7, 1] which is consistent with the model used in [6].
We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the recursively enumerable sets using Fourier coefficients of recursive analytic functions that are generated by differential equations and elementary operations. (C) 2010 Elsevier B.V. All rights reserved.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.