Order conditions for Volterra Runge�Kutta methods

• Autores: Roberto Garrappa
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 5, 2010, págs. 561-573
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.02.004
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• Resumen

  • We consider Runge�Kutta methods for second-kind Volterra Integral Equations with weakly singular kernel. Order conditions, whose number and structure depend on the singularity of the equation, are derived in a recursive manner using an approach originally devised by P. Albrecht for Ordinary Differential Equations. Order conditions are hence generated, in an automatic way, by means of a symbolic algorithm and some numerical experiments are presented.