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Solving Problems Numerically
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In this article (Solving Problems Numerically), we look at solving two
problems numerically. The problems solved are relatively simple and
actually have closed-form solutions. We use simple examples to illustrate
the steps involved in obtaining numerical solutions without getting too involved
in the mathematics. And, by having closed-form, or exact, solutions
available, it gives us something to check our computer programming techniques.
The first problem (one-dimensional) requires the determination of a model rocket
engine's burn time in order to achieve a desired altitude. The second
problem (two-dimensional) is a numerical implementation of converting from
rectangular to polar coordinates. While solving these problems, we will
address some of common problems encountered when implementing numerical
(computer-based) solutions. Suggestions for using the example problems and
potential expansions of the problems are addressed.
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