Added a few paragraphs to the paper draft.

paper/paper.md

@@ -18,6 +18,16 @@ bibliography: paper.bib
 
 This package provides a general-purpose integro-differential equation solver based on an iterative algorithm devised by Gelmi and Jorquera [@Gelmi2014].
 Integro-differential equations appear in many contexts, particularly when trying to describe a system whose current behavior depends on its own history.
+A good example is in electronics, where the differential equation for a circuit made only of resistors, capacitors, and inductors can be written in a mixed form where both the derivative and integral of the current appear (for the inductors and capacitors respectively).
+
+Very simple IDEs like those in electronics can often by solved by Laplace transformation (or turned into double-differential form and solved by Fourier transform or any number of other techniques).
+Finding analytic solutions for more complicated IDEs is an area of active research and tends to require a special approach for each one.
+Even these techniques often produce non-closed forms for the result.
+
+In 2014, Gelmi and Jorquera [@Gelmi2014] published a simple iterative algorithm for finding the solution to a fairly generic integro-differential equation.
+IDESolver implements a modified and expanded version of this algorithm.
+It can handle both real- and complex-valued IDEs, and uses a slightly different error estimate.
+
 
 # References