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Discretization methods for ordinary differential equations are usually not exact; they commit an error at every step of the algorithm. All these errors combine to form the global error, which is the error in the final result. The global error is the subject of this thesis. In the first half of the thesis, accurate a priori estimates of the global error are(More)
We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE can be decomposed into several pieces and each of them is integrable. This class of integrators are explicit, simple(More)
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)
In this paper we show how to build high order integrators for solving ordinary diierential equations by composition of low order methods and using the processing technique. From a basic p-th order method, p , one can obtain high order integrators in the processed form n = P K P ?1 (n > p) being both the processor P and the kernel K compositions of the basic(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)
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)