Abstract
As we have already mentioned, most initial value problems do not have “closed-form” solutions. To obtain approximate solutions, especially in applications, one must resort to numerical methods. This, in fact, is how PHASER generates the orbits you will see in the illustrations. In this chapter, we will briefly discuss what it means to solve an initial value problem (1.1–2) using numerical algorithms, and also give some practical guidelines. For a good elementary introduction to this subject, you should start with Chapter 8 of Boyce & DiPrima [1977], which contains a discussion of the algorithms used by PHASER. If you wish, you can follow this up with more advanced books such as Conte & deBoor [1972] and Gear [1971].
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© 1989 Springer-Verlag New York Inc.
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Koçak, H. (1989). Numerical Methods. In: Differential and Difference Equations through Computer Experiments. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3610-8_2
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DOI: https://doi.org/10.1007/978-1-4612-3610-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96918-3
Online ISBN: 978-1-4612-3610-8
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