On Non-Oscillating Integrals for Computing Inhomogeneous Airy Functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2001
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| _version_ | 1866915560052228096 |
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| author | Gil, Amparo Segura, Javier Temme, Nico M. |
| author_facet | Gil, Amparo Segura, Javier Temme, Nico M. |
| contents | Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm1/π$. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods from asymptotics, the standard integral representations of the Scorer functions are modified in order to obtain non-oscillating integrals for complex values of $z$. In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0109187 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | On Non-Oscillating Integrals for Computing Inhomogeneous Airy Functions Gil, Amparo Segura, Javier Temme, Nico M. Numerical Analysis Classical Analysis and ODEs 33C10, 41A60, 65D20 Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm1/π$. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane. By using steepest descent methods from asymptotics, the standard integral representations of the Scorer functions are modified in order to obtain non-oscillating integrals for complex values of $z$. In this way stable representations for numerical evaluations of the functions are obtained. The methods are illustrated with numerical results. |
| title | On Non-Oscillating Integrals for Computing Inhomogeneous Airy Functions |
| topic | Numerical Analysis Classical Analysis and ODEs 33C10, 41A60, 65D20 |
| url | https://arxiv.org/abs/math/0109187 |