High-order collocation methods for singular Volterra functional equations of neutral type

• Autores: Hermann Brunner
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 57, Nº. 5-7, 2007, págs. 533-548
• Idioma: inglés
• DOI: 10.1016/j.apnum.2006.07.006
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• Resumen

  • In the first part of this paper we present a survey of recent results on the attainable order of (super-) convergence of collocation solutions for systems of Volterra functional integro-differential equations with weakly singular kernels ka and variable delay functions ?(t)=t-t(t). Related functional equations and theoretical and computational aspects of collocation methods for their solution are also described. The paper concludes with comments on ongoing and possible future work.