Dajana Conte

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A very general class of Runge-Kutta methods for Volterra integral equations of the second kind is analyzed. Order and stage order conditions are derived for methods of order p and stage order q = p up to the order four. We also investigate stability properties of these methods with respect to the basic and the convolution test equations. The systematic(More)
It is the purpose of this paper to provide an acceleration of waveform relaxation (WR) methods for the numerical solution of large systems of ordinary differential equations. The introduced technique is based on the employ of graphics processing units (GPUs) in order to speed-up the numerical integration process. A CUDA solver based on WR-Picard, WR-Jacobi(More)
Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability(More)