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. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
Order conditions for Volterra Runge-Kutta methods
GARRAPPA, Roberto
2010-01-01
Abstract
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. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.File in questo prodotto:
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