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This paper gives an error analysis of the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of multi-particle time-dependent Schrödinger equations. The MCTDH method approximates the multivariate wave function by a linear combination of products of univariate functions and replaces the high-dimensional linear Schrödinger… (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)
It is the purpose of this talk to introduce a family of diagonally–implicit continuous methods for the numerical integration of Volterra Integral Equations , which are obtained as a modification of the class of two-step collo-cation methods introduced in [1, 2]. The derived methods result from the choice of suitable conditions to be satisfied by the… (More)
In this paper the stability properties of fast numerical methods for Volterra integral equations of Hammerstein type with respect to significant test equations are investigated.
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)