Just a point of history. The "dynamic approach" to IS-LM is present in the 
work of Samuelson (1941), Modigliani (1944) and Klein (1947) in the form of 
dynamic systems based upon both differential and difference equations in the 
case of Samuelson (1941), that later became Ch IX of "Foundations", and in 
the dynamical model (difference equations) in Modigliani (1944: 62-64, eg. 
p. 63, equations 2.1-2.6).

But, as Dave Colander correctly notes, it is difficult to "hang" things such 
as difference and differential euqations onto a two-dimensional notional 
diagram, and thus the textbook writers never bothered with the richer 
dynamic framework provided by Samuelson, Modigliani and Klein, until 
insightful authors such as George Horwich realized that something important 
was missing from the original Harrod-Meade-Hicks euqational-diagrammatic 
SILL framework....

Warren Young