Related papers: Fourth-order leapfrog algorithms for numerical tim…

We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…

We show in this paper that third- and fourth-order low storage Runge-Kutta algorithms can be built specifically for quadratic nonlinear operators, at the expense of roughly doubling the time needed for evaluating the temporal derivatives.…

The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers and holds immense promise for advancing the fields of physical and computer sciences, with applications spanning…

Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order…

In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…

Forward time step integrators are splitting algorithms with only positive splitting coefficients. When used in solving physical evolution equations, these positive coefficients correspond to positive time steps. Forward algorithms are…

The structural flexibility of the exponential propagation iterative methods of Runge-Kutta type (EPIRK) enables construction of particularly efficient exponential time integrators. While the EPIRK methods have been shown to perform well on…

Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially…

The numerical efficiency of different schemes for solving the Liouville-von Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge-Kutta scheme in two different…

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…

Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…

In this article, a three-time levels compact scheme is proposed to solve the partial integro-differential equation governing the option prices under jump-diffusion models. In the proposed compact scheme, the second derivative approximation…

The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…

Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…

Study of far-from-equilibrium thermalization dynamics in quantum materials, including the dynamics of different types of quasiparticles, is becoming increasingly crucial. However, the inherent complexity of either the full quantum…

Product formula methods, particularly the second-order Suzuki decomposition, are an important tool for simulating quantum dynamics on quantum computers due to their simplicity and unitarity preservation. While higher-order schemes have been…

One of the most promising applications of near-term quantum computing is the simulation of quantum systems, a classically intractable task. Quantum simulation requires computationally expensive matrix exponentiation; Trotter-Suzuki…

Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains, via…

We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from…