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We are concerned with the numerical solution obtained by splitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. It has been demonstrated that this second-order barrier can be overcome by using splitting methods with complex-valued… (More)

We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy of the integrator and/or reducing the size of its error constants; order and error constant are relevant concepts in… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t We consider Magnus integrators to solve linear-quadratic N-player… (More)

The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the numerical integration of this problem using the imbedding formulation. An algorithm to implement this explicit method in an efficient way… (More)

We provide a theoretical analysis of the processing technique for the numerical integration of ODEs. We get the effective order conditions for processed methods in a general setting so that the results obtained can be applied to different types of numerical integrators. We also propose a procedure to approximate the postprocessor such that its evaluation is… (More)

A comprehensive linear stability analysis of splitting methods is carried out by means of a 2 × 2 matrix K(x) with polynomial entries (the stability matrix) and the stability polynomial p(x) (the trace of K(x) divided by two). An algorithm is provided for determining the coefficients of all possible time-reversible splitting schemes for a prescribed… (More)

We construct numerical integrators for differential equations up to order 12 obtained by composition of basic integrators. The following cases are considered: (i) composition for a system separable in two solvable parts, (ii) composition using as basic methods a first-order integrator and its adjoint, (iii) composition using second-order symmetric methods,… (More)