Most of the physical processes arising in nature are modeled by either
ordinary or partial differential equations. From the point of view of analog
computability, the existence of an effective way to obtain solutions of these
systems is essential. A pioneering model of analog computation is the General
Purpose Analog Computer (GPAC), introduced by Shannon as a model of the
Differential Analyzer and improved by Pour-El, Lipshitz and Rubel, Costa and
Gra\c{c}a and others. Its power is known to be characterized by the class of
differentially algebraic functions, which includes the solutions of initial
value problems for ordinary differential equations. We address one of the
limitations of this model, concerning the notion of approximability, a
desirable property in computation over continuous spaces that is however absent
in the GPAC. In particular, the Shannon GPAC cannot be used to generate
non-differentially algebraic functions which can be approximately computed in
other models of computation. We extend the class of data types using networks
with channels which carry information on a general complete metric space $X$;
for example $X=C(R,R)$, the class of continuous functions of one real (spatial)
variable. We consider the original modules in Shannon's construction
(constants, adders, multipliers, integrators) and we add \emph{(continuous or
discrete) limit} modules which have one input and one output. We then define an
L-GPAC to be a network built with $X$-stream channels and the above-mentioned
modules. This leads us to a framework in which the specifications of such
analog systems are given by fixed points of certain operators on continuous
data streams. We study these analog systems and their associated operators, and
show how some classically non-generable functions, such as the gamma function
and the zeta function, can be captured with the L-GPAC.
