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Difference equations have been increasingly used as mathematical models in
many disciplines including genetics, eipdemiology, ecology, physiology, neural
networks, psychology, engineering, physics, chemistry and social sciences.
Their amenability to computerization and their mathematical simplicity have
attracted researchers from a wide range of disciplines. As we will see in Section
1.2, difference equations are generated by maps (functions). Section 1.3
illustrates how discretizing a differential equation would yeild a difference
equation. Discretization algorithms are part of a discipline called numerical
analysis which belong to both mathematics and computer science. As most
differential equations are unsolvable, one needs to resort to computers for
help. However, computers understand only recursions or difference equations;
thus the need to discretize differential equations.
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