Summary
Non-linear second-order differential equations whose solutions are the
elliptic functions sn(t, k), cn(t, k) and dn(t, k) are investigated. Using Mathematica,
high precision numerical solutions are generated. From these data, Fourier
coefficients are determined yielding approximate formulas for these nonelementary
functions that are correct to at least 11 decimal places. These
formulas have the advantage over numerically generated data that they are
computationally efficient over the entire real line. This approach is seen as
further justification for the early introduction of Fourier series in the undergraduate
curriculum, for by doing so, models previously considered hard or
advanced, whose solution involves elliptic functions, can be solved and plotted
as easily as those models whose solutions involve merely trigonometric or other
elementary functions.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:tut/oai:encore.tut.ac.za:d1001987 |
| Date | 31 July 2003 |
| Creators | Fay, TH |
| Publisher | International Journal of Mathematical Education in Science and Technology |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | |
| Rights | International Journal of Mathematical Education in Science and Technology |
| Relation | Taylor & Francis |
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