A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function U (a, z) in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly efficient method based on a fourth-order fixed point method with...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/36372 |
| Acceso en línea: | https://hdl.handle.net/10902/36372 |
| Access Level: | acceso abierto |
| Palabra clave: | Parabolic cylinder functions Complex zeros Fixed point methods Matlab software |
| Sumario: | A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function U (a, z) in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly efficient method based on a fourth-order fixed point method with the parabolic cylinder functions computed by Taylor series and carefully selected steps, to compute the rest of the zeros. For |a| small, the asymptotic approximations are complemented with a few fixed point iterations requiring the evaluation of U (a, z) and U' (a,z) in the region where the complex zeros are located. Liouville Green expansions are derived to enhance the performance of a computational scheme to evaluate U (a, z) and U' (a,z) in that region. Several tests show the accuracy and efficiency of the numerical algorithm. |
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