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A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…

Statistical Mechanics · Physics 2009-11-07 Igor Omelyan , Ihor Mryglod , Reinhard Folk

Single-stage or single-step high-order temporal discretizations of partial differential equations (PDEs) have shown great promise in delivering high-order accuracy in time with efficient use of computational resources. There has been much…

Numerical Analysis · Mathematics 2021-03-02 Youngjun Lee , Dongwook Lee , Adam Reyes

We study the ODE/IM correspondence between two-dimensional $WA_{r}$/$WD_{r}$-type conformal field theories and the higher-order ordinary differential equations (ODEs) obtained from the affine Toda field theories associated with…

High Energy Physics - Theory · Physics 2024-12-09 Katsushi Ito , Mingshuo Zhu

We present a shifted-geodesic framework for computing gravitational-wave fluxes from spinning test bodies moving on bound orbits of Kerr black holes. The method provides a simple and efficient means of evaluating energy and angular momentum…

General Relativity and Quantum Cosmology · Physics 2026-03-13 Lisa V. Drummond , Scott A. Hughes , Viktor Skoupý , Philip Lynch , Gabriel Andres Piovano

Although the gravitational waves observed by advanced LIGO and Virgo are consistent with compact binaries in a quasi-circular inspiral prior to coalescence, eccentric inspirals are also expected to occur in Nature. Due to their complexity,…

General Relativity and Quantum Cosmology · Physics 2018-12-05 Blake Moore , Travis Robson , Nicholas Loutrel , Nicolas Yunes

In this paper we present a new public code, named $ynogkm$, for the fast calculation of time-like geodesics in the Kerr-Newmann (K-N) spacetime, which is a direct extension of $ynogk$ calculating null geodesics in a Kerr spacetime.…

General Relativity and Quantum Cosmology · Physics 2015-06-17 Xiao-lin Yang , Jian-cheng Wang

We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex…

Mathematical Software · Computer Science 2016-07-06 Fredrik Johansson

We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…

Numerical Analysis · Mathematics 2025-08-29 Zhenyu Zhao , Yanfei Wang , Xinran Liu

We report on the status an ab initio computation of the time-like splitting functions at next-to-next-to-leading order in QCD. Time-like splitting functions govern the collinear kinematics of inclusive hadron production in $e^+e^-$…

High Energy Physics - Phenomenology · Physics 2016-01-15 O. Gituliar

Extreme mass-ratio inspirals are among the key sources of gravitational waves for the Laser Interferometer Space Antenna space-based gravitational-wave detector. Achieving sufficient accuracy in the gravitational-wave template for these…

General Relativity and Quantum Cosmology · Physics 2025-11-14 Gabriel Andres Piovano , Christiana Pantelidou , Jake Mac Uilliam , Vojtěch Witzany

This paper presents a novel framework for Jacobian computation in motion optimization problems involving multi-link systems, where physical quantities are represented using higher-order time derivatives. In motion optimization of robots and…

Robotics · Computer Science 2026-05-18 Taiki Ishigaki , Ko Ayusawa , Eiichi Yoshida

A high-order space-time flux reconstruction (FR) method has been developed to solve conservation laws on moving domains. In the space-time framework, the moving domain simulation is similar to that on a stationary domain, except that the…

Numerical Analysis · Mathematics 2024-09-24 Meilin Yu

We classify radial timelike geodesic motion of the exterior non-extremal Kerr spacetime by performing a taxonomy of inequivalent root structures of the first order radial geodesic equation using a novel compact notation and by implementing…

General Relativity and Quantum Cosmology · Physics 2022-02-09 Geoffrey Compère , Yan Liu , Jiang Long

Variable-order time-fractional wave equations provide a flexible model for wave phenomena with evolving memory effects and anomalous temporal dynamics. Their numerical approximation is challenging because the variable-order fractional…

Numerical Analysis · Mathematics 2026-05-26 Lu Zhang

Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…

Numerical Analysis · Computer Science 2014-04-01 Nail A. Gumerov , Ramani Duraiswami

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…

Mathematical Physics · Physics 2015-05-14 John T. Conway , Howard S. Cohl

One of the most important geodesics in a black-hole spacetime is the marginally bound spherical orbit. This critical geodesic represents the innermost spherical orbit which is bound to the central black hole. The radii $r_{\text{mb}}({\bar…

General Relativity and Quantum Cosmology · Physics 2017-07-19 Shahar Hod

Accurate reconstruction of piecewise-smooth functions from a finite number of Fourier coefficients is an important problem in various applications. The inherent inaccuracy, in particular the Gibbs phenomenon, is being intensively…

Classical Analysis and ODEs · Mathematics 2012-11-12 Dmitry Batenkov , Yosef Yomdin

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…

High Energy Physics - Phenomenology · Physics 2010-05-28 Mathias Wagner , Andrea Walther , Bernd-Jochen Schaefer

The explicit split-operator algorithm has been extensively used for solving not only linear but also nonlinear time-dependent Schr\"{o}dinger equations. When applied to the nonlinear Gross-Pitaevskii equation, the method remains…

Chemical Physics · Physics 2024-09-26 Julien Roulet , Jiří Vaníček