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Since the expense of the numerical integration of large scale dynamical systems is often computationally prohibitive, model reduction methods, which approximate such systems by simpler and much lower order ones, are often employed to reduce…
Controlling individual elements of coupled resonator systems poses a significant challenge, as conventional real-frequency pulses suffer from inefficiency and crosstalk, limiting fidelity and scalability. To address this challenge, we…
We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
We present an equation-free computational approach to the study of the coarse-grained dynamics of {\it finite} assemblies of {\it non-identical} coupled oscillators at and near full synchronization. We use coarse-grained observables which…
Numerical algorithms based on variational and symplectic integrators exhibit special features that make them promising candidates for application to general relativity and other constrained Hamiltonian systems. This paper lays part of the…
Frequency response optimized integrators considering second order derivative are proposed in this paper. Based on the proposed numerical integrators, and others which also consider second order derivative, this paper puts forward a novel…
This paper is a survey on exponential integrators to solve cubic-quintic complex Ginzburg-Landau equations and related stiff problems. In particular, we are interested in accurate computation near the pulsating and exploding soliton…
Strong light-matter coupling to form exciton- and vibropolaritons is increasingly touted as a powerful tool to alter the fundamental properties of organic materials. It is proposed that these states and their facile tunability can be used…
The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems is an open and important problem in both numerical analysis and computing in science and engineering, as explicit integrators are usually more…
The model of coupled oscillators plays an important role in modern physics. It is used for description of various processes: from vibrations atoms in solid states to electromagnetic oscillations in slow-wave structures. The model with…
In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally…
The numerical evaluation of integrals of the form \begin{align*} \int_a^b f(x) e^{ikg(x)}\,dx \end{align*} is an important problem in scientific computing with significant applications in many branches of applied mathematics, science and…
Power system simulations that extend over a time period of minutes, hours, or even longer are called extended-term simulations. As power systems evolve into complex systems with increasing interdependencies and richer dynamic behaviors…
Recently a new class of numerical integration methods -- ``mixed variable symplectic integrators'' -- has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of…
We consider the numerical simulation of Hamiltonian systems of ordinary differential equations. Two features of Hamiltonian systems are that energy is conserved along trajectories and phase space volume is preserved by the flow. We want to…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
Obreshkov-like numerical integrators have been widely applied to power system transient simulation. Misuse of the numerical integrators as numerical differentiators may lead to numerical oscillation or bias. Criteria for Obreshkov-like…
The unitary evolution can be represented by a finite product of exponential operators. It leads to a perturbative expression of the density operator of a close system. Based on the perturbative expression scheme, we present a entanglement…