Listar por autoría "31a75131-2879-4ab1-bbac-c669aa5c16b2"
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On the Linear Stability of Splitting Methods
Springer Verlag (2008)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 ... -
Optimized high-order splitting methods for some classes of parabolic equation
American Mathematical Society (2013)Weareconcernedwiththenumericalsolutionobtainedbysplitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. ...
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Preface for the special issue “Geometric numerical integration, twenty-five years later”
Taylor and Francis (2023)
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Runge–Kutta–Nyström symplectic splitting methods of order 8
Elsevier (2022-12)Different families of Runge–Kutta–Nyström (RKN) symplectic splitting methods of order 8 are presented for second-order systems of ordinary differential equations and are tested on numerical examples. They show a better ...
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Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex
American Institute of Physics (AIP Publishing LLC) (2013)The Schrödinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional ...
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Splitting and composition methods in the numerical integration of differential equations
Sociedad Española de Matemática Aplicada (2008)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 ...
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Splitting and composition methods with embedded error estimators
Elsevier (2019-12)We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, ...
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Splitting methods in the numerical integration of non-autonomous dynamical systems
Springer (2012)We present a procedure leading to efficient splitting schemes for the time integration of explicitly time dependent partitioned linear differential equa- tions arising when certain partial differential equations are ...
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Splitting methods with complex coefficients
Sociedad Española de Matemática Aplicada (2010)Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with ...
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Symmetric-conjugate splitting methods for linear unitary problems
Springer (2023-11-10)We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve ...
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Symmetrically processed splitting integrators for enhanced hamiltonian monte carlo sampling
Society for Industrial and Applied Mathematics (2021-09-23)We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver five times as many accepted proposals as ...
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Symplectic integrators for second-order linear non-autonomous equations
Elsevier (2018-03)Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they ...
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Symplectic propagators for the Kepler problem with time-dependent mass
Springer (2019-06)New numerical integrators specifically designed for solving the two-body gravitational problem with a time-varying mass are presented. They can be seen as a generalization of commutator-free quasi-Magnus exponential ...
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Symplectic time-average propagators for the Schrodinger equation with a time-dependent Hamiltonian
AIP Publishing (2017-03)Several symplectic splitting methods of orders four and six are presented for the step-by-step time numerical integration of the Schrödinger equation when the Hamiltonian is a general explicitly time-dependent real operator. ...
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The Magnus expansion and some of its applications
Elsevier (2009)Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. ...
