相关论文: 2N-storage Runge-Kutta methods: Order conditions, …

We develop continuous-stage Runge-Kutta-Nystr\"{o}m (csRKN) methods for solving second order ordinary differential equations (ODEs) in this paper. The second order ODEs are commonly encountered in various fields and some of them can be…

We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…

Through the introduction of a new electron spin transport mechanism, a 2D donor electron spin quantum computer architecture is proposed. This design addresses major technical issues in the original Kane design, including spatial…

The parameterization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science and planetology. In the presence of…

The residual-based variational multiscale (VMS) formulation has achieved remarkable success in large-eddy simulation of turbulent flows. However, its temporal discretization has largely remained limited to second-order implicit schemes. The…

In this article, a family of two- and three-stage explicit multiquadric (MQ) and inverse multiquadric (IMQ) radial basis functions (RBFs) Runge-Kutta methods are introduced for solving ordinary differential equations. These methods are…

We present a novel and general methodology for building second-order finite volume implicit-explicit Runge-Kutta numerical schemes for solving two-dimensional financial parabolic PDEs with mixed derivatives. The methods achieve second-order…

Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical…

A method for storing quantum information is presented for $3$-level atomic systems interacting dipolarly with a single radiation field. The method involves performing simple local SU(2) rotations on the Hamiltonian. Under equal detuning,…

Important quantum algorithm routines allow the implementation of specific quantum operations (a.k.a. gates) by combining basic quantum circuits with an iterative structure. In this structure, the number of repetitions of the basic circuit…

We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary…

This work constructs and analyzes new efficient high-order two-derivative diagonally implicit Runge--Kutta (TDDIRK) schemes with optimized phase errors. Specifically, we present a convergence result for TDDIRK methods and investigate their…

The superconducting ground state in many two-dimensional materials can be created or destroyed through quantum phase transitions (QPTs) controlled by non-thermal parameters such as carrier density or magnetic field. While various mechanisms…

Recently Watanabe has given an algorithm to compute a bijection, that he calls (quantum) Littlewood-Richardson (LR) map (or quantum LR rule of type AII), between semi-standard Young tableaux of shape a partition with at most $2n$ parts and…

This paper investigates, a new class of fractional order Runge-Kutta (FORK) methods for numerical approximation to the solution of fractional differential equations (FDEs). By using the Caputo generalizedTaylor formula and the total…

Many HPC applications that solve differential equations rely on the Runge-Kutta family of methods for time integration. Among these methods, the fourth-order accurate RK4 scheme is especially popular. This time integration scheme requires…

This note explores in more details instabilities of explicit super-time-stepping schemes, such as the Runge-Kutta-Chebyshev or Runge-Kutta-Legendre schemes, noticed in the litterature, when applied to the Heston stochastic volatility model.…

We focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary…

The work deals with two major topics concerning the numerical analysis of Runge-Kutta-like (RK-like) methods, namely their stability and order of convergence. RK-like methods differ from additive RK methods in that their coefficients are…

The capacitive couplings between gate-defined quantum dots and their gates vary considerably as a function of applied gate voltages. The conversion between gate voltages and the relevant energy scales is usually performed in a regime of…