相关论文: Proper Selection of Obreshkov-Like Numerical Integ…

We introduce an efficient numerical method for second order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory…

Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…

We present a fourth order convergent (2+1) numerical code to solve the Teukolsky equation in the time domain. Our approach is to rewrite the Teukolsky equation as a system of first order differential equations. In this way we get a system…

Recording reliably extracellular neural activities isan essential prerequisite for the development of bioelectronicsand neuroprosthetic applications. Recently, a fully differential,2-stage, integrating pre-amplifier was proposed for…

We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr\"odinger equation. We prove that a particular class of integrators are conjugate to unitary methods for…

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…

Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence…

A mathematical model of oscillatory systems control with liquid dampers is considered which differs from the classical ones by replacing the first derivative of such a fractional derivative that is between numbers 0 and 2 other than unity.…

We introduce two exponential-type integrators for the "good" Bousinessq equation. They are of orders one and two, respectively, and they require lower regularity of the solution compared to the classical exponential integrators. More…

We introduce new numerical integration operators which compose the mass and stiffness matrices of a modified spectral element method for simulation of elastic wave propagation. While these operators use the same quadrature nodes as does the…

We introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations themselves are driven by a Stratonovich noise. Applications…

Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these…

We show that Oscillator Ising Machines (OIMs) are prime candidates for use as neuromorphic machine learning processors with Equilibrium Propagation (EP) based on-chip learning. The inherent energy gradient descent dynamics of OIMs, combined…

A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is…

This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The…

Fractional Pontryagin's systems emerge in the study of a class of fractional optimal control problems but they are not resolvable in most cases. In this paper, we suggest a numerical approach for these fractional systems. Precisely, we…

We investigate time-adaptive Magnus-type integrators for the numerical approximation of a Mott transistor. The rapidly attenuating electromagnetic field calls for adaptive choice of the time steps. As a basis for step selection,…

Fractional order derivatives and integrals (differintegrals) are viewed from a frequency-domain perspective using the formalism of Riesz, providing a computational tool as well as a way to interpret the operations in the frequency domain.…

We use the formerly derived explicit analytical expressions for the conductivity of nanostructured superconductors supercooled below the critical temperature in electric field. Computer simulations reveal that the negative differential…