Hybrid solvers for composition and splitting methods

Sofroniou, Mark; Spaletta, Giulia

doi:10.1016/j.cam.2005.03.011

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…To compare various schemes, we use the coefficient plug-in mechanism of a new framework for composed numerical integrators in Mathematica [18]. The large number of stages used by high order methods requires careful implementation to reduce cumulative roundoff error.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Derivation of symmetric composition constants for symmetric integrators

Sofroniou

Spaletta

2005

Optimization Methods and Software

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This work focuses on the derivation of composition methods for the numerical integration of ordinary differential equations, which give rise to very challenging optimization problems. Composition is a useful technique for constructing high order approximations, while conserving certain geometric properties. We survey existing composition methods and describe results of an intensive numerical search for new methods. Details of the search procedure are given along with numerical examples, which indicate that the new methods perform better than previously known methods. Some insight into the location of global minima for these problems is obtained as a result.

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Section: Numerical Experimentsmentioning

confidence: 99%

Derivation of symmetric composition constants for symmetric integrators

Sofroniou

Spaletta

2005

Optimization Methods and Software

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Stability by order stars for non-linear theta-methods based on means

Villatoro

2010

International Journal of Computer Mathematics

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The linear stability analysis of non-linear one-step methods based on means is studied by means of the concept of stability regions and order stars. Concretely, non-linear θ -methods based on harmonic, contraharmonic, quadratic, geometric, Heronian, centroidal and logarithmic means are considered. Their stability diagrams and order stars show their A-stability for θ ≥ 1/2, and L-stability in some cases. Order stars in the Riemann surface are a requirement for non-linear one-step methods. The advantages and disadvantages of this technique are presented.

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Semi-Explicit Composition Methods in Memcapacitor Circuit Simulation

Butusov

Ostrovskii

Каримов

et al. 2019

International Journal of Embedded and Real-Time Communication Systems

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Composition algorithms make up a prospective class of methods for solving ordinary differential equations. Their main advantage is an ability to retain some properties of the simulated continuous systems, e.g. phase space volume. Meanwhile, computational costs of composition solvers for non-Hamiltonian systems are high because the implicit midpoint rule should be used as a basic method. This also complicates the development of embedded applications based on the numerical solution of ODEs, such as hardware chaos generators. In this article, a new semi-explicit composition methods are proposed. The stability regions for different composition algorithms were plotted and a memcapacitor circuit was studied as a test problem. Computational experiments reveal the superior properties of semi-explicit composition algorithms as a hardware-targeted ODE solvers. The obtained results imply that the development of semi-explicit composition algorithms is a step towards construction a new generation of simulation software for nonlinear dynamical systems and embedded chaos generators.

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Hybrid solvers for composition and splitting methods

Cited by 3 publications

References 20 publications

Derivation of symmetric composition constants for symmetric integrators

Derivation of symmetric composition constants for symmetric integrators

Stability by order stars for non-linear theta-methods based on means

Semi-Explicit Composition Methods in Memcapacitor Circuit Simulation

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