Related papers: Time Symmetrization Meta-Algorithms
We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…
Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…
This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…
In the context of non-Hermitian quantum mechanics, many systems are known to possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related to its adjoint H^{{\dag}} via the relation, H^{{\dag}}=PTHPT . We propose a…
We consider the External Clock Synchronization problem in dynamic sensor networks. Initially, sensors obtain inaccurate estimations of an external time reference and subsequently collaborate in order to synchronize their internal clocks…
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of…
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…
It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…
We develop a class of C1-continuous time integration methods that are applicable to conservative problems in elastodynamics. These methods are based on Hamilton's law of varying action. From the action of the continuous system we derive a…
Momentum methods for convex optimization often rely on precise choices of algorithmic parameters, based on knowledge of problem parameters, in order to achieve fast convergence, as well as to prevent oscillations that could severely…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
A non-${\cal{PT}}$-symmetric Hamiltonian system of a Duffing oscillator coupled to an anti-damped oscillator with a variable angular frequency is shown to admit periodic solutions. The result implies that ${\cal{PT}}$-symmetry of a…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…