High performance parallel numerical methods for Volterra equations with weakly singular kernels

• Autores: Giovanni Capobianco, Dajana Conte, Ida Del Prete
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 228, Nº 2, 2009 (Ejemplar dedicado a: Innovative methods for solving evolutionary problems), págs. 571-579
• Idioma: inglés
• DOI: 10.1016/j.cam.2008.03.027
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• Resumen

  • Non-stationary discrete time waveform relaxation methods for Abel systems of Volterra integral equations using fractional linear multistep formulae are introduced. Fully parallel discrete waveform relaxation methods having an optimal convergence rate are constructed. A significant expression of the error is proved, which allows us to estimate the number of iterations needed to satisfy a prescribed tolerance and allows us to identify the problems where the optimal methods offer the best performance. The numerical experiments confirm the theoretical expectations.