Abstract
At the heart of many problems in mathematics, physics, and engineering lies the ordinary differential equation or its numerical equivalent, the ordinary finite difference equation. Ordinary differential equations arise not only in countless direct applications, but also occur indirectly, as reductions of partial differential equations (by way of separation of variables or by transform techniques for example; cf. Chaps. 9, 11). Likewise, the probably less familiar difference equations are of inherent interest (in probability, statistics, economics, etc.) but also appear as recurrence relations in connection with differential equations or as numerical approximations to differential equations.
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