Approximate solution of Abel integral equation in Daubechies wavelet basis

• Autores: Jyotirmoy Mouley, M. M. Panja, B. N. Mandal
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 23, Nº. 2, 2021, págs. 245-264
• Idioma: inglés
• DOI: 10.4067/S0719-06462021000200245
• Enlaces
  • Texto completo
• Resumen
  • español

    RESUMEN Este artículo presenta un nuevo método computacional para resolver la ecuación integral de Abel (tanto de primer como de segundo tipo). El esquema numérico está basado en aproximaciones en la base de ondeletas de Daubechies. Se emplean las propiedades de las funciones de escala de Daubechies para reducir una ecuación integral a la solución de un sistema algebraico de ecuaciones. Se entrega el análisis de error asociado con el método. El método es ilustrado con algunos ejemplos donde el método presentado funciona bien en baja resolución.

  • English

    ABSTRACT This paper presents a new computational method for solving Abel integral equation (both first kind and second kind). The numerical scheme is based on approximations in Daubechies wavelet basis. The properties of Daubechies scale functions are employed to reduce an integral equation to the solution of a system of algebraic equations. The error analysis associated with the method is given. The method is illustrated with some examples and the present method works nicely for low resolution.

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