252 research outputs found
Sixth-order symmetric and symplectic exponentially fitted Runge–Kutta methods of the Gauss type
AbstractThe construction of exponentially fitted Runge–Kutta (EFRK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is considered. Based on the symplecticness, symmetry, and exponential fitting properties, two new three-stage RK integrators of the Gauss type with fixed or variable nodes, are obtained. The new exponentially fitted RK Gauss type methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(λt),exp(−λt)}, λ∈C, and in particular {sin(ωt),cos(ωt)} when λ=iω, ω∈R. The algebraic order of the new integrators is also analyzed, obtaining that they are of sixth-order like the classical three-stage RK Gauss method. Some numerical experiments show that the new methods are more efficient than the symplectic RK Gauss methods (either standard or else exponentially fitted) proposed in the scientific literature
Explicit symplectic integrator for particle tracking in s-dependent static electric and magnetic fields with curved reference trajectory
We describe a method for symplectic tracking of charged particles through
static electric and magnetic fields. The method can be applied to cases where
the fields have a dependence on longitudinal as well as transverse position,
and where the reference trajectory may have non-zero curvature. Application of
the method requires analytical expressions for the scalar and vector
potentials: we show how suitable expressions, in the form of series analogous
to multipole expansions, can be constructed from numerical field data, allowing
the method to be used in cases where only numerical field data are available.Comment: 17 page
SMD-based numerical stochastic perturbation theory
The viability of a variant of numerical stochastic perturbation theory, where
the Langevin equation is replaced by the SMD algorithm, is examined. In
particular, the convergence of the process to a unique stationary state is
rigorously established and the use of higher-order symplectic integration
schemes is shown to be highly profitable in this context. For illustration, the
gradient-flow coupling in finite volume with Schr\"odinger functional boundary
conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory.
The scaling behaviour of the algorithm turns out to be rather favourable in
this case, which allows the computations to be driven close to the continuum
limit.Comment: 35 pages, 4 figures; v2: corrected typos, coincides with published
versio
エネルギー関数を持つ発展方程式に対する幾何学的数値計算法
学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 松尾 宇泰, 東京大学教授 中島 研吾, 東京大学准教授 鈴木 秀幸, 東京大学准教授 長尾 大道, 東京大学准教授 齋藤 宣一University of Tokyo(東京大学
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