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| Content Provider | ACM Digital Library |
|---|---|
| Author | Lozier, D. W. Fabijonas, B. R. Olver, F. W. J. |
| Copyright Year | 2004 |
| Abstract | We describe a method by which one can compute the solutions of Airy's differential equation, and their derivatives, both on the real line and in the complex plane. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. We give details involved in obtaining all of the parameter values, and we control the truncation errors rigorously. Using the same computational methods, we describe an algorithm that computes the zeros and associated values of the Airy functions and their derivatives, and the modulus and phase functions on the negative real axis. |
| Starting Page | 471 |
| Ending Page | 490 |
| Page Count | 20 |
| File Format | |
| ISSN | 00983500 |
| e-ISSN | 15577295 |
| DOI | 10.1145/1039813.1039818 |
| Volume Number | 30 |
| Issue Number | 4 |
| Journal | ACM Transactions on Mathematical Software (TOMS) |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 2004-12-01 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Asymptotic expansions Algorithms for special functions Differential equations Error analysis Real and complex Airy functions Zeros |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Software |
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