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In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…

Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that…

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…

How to accurately solve time-dependent Schr\"odinger equation is an interesting and important problem. Here, we propose a novel method to obtain the exact Floquet solutions of the Schr\"odinger equation for periodically driven systems by…

Quantum dynamics, typically expressed in the form of a time-dependent Schr\"odinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission…

We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…

This paper investigates the application of a fast-wave slow-wave spectral deferred correction time-stepping method (FWSW-SDC) to the compressible Euler equations. The resulting model achieves arbitrary order accuracy in time, demonstrating…

The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose…

The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the…

We have developed the technique of a quantum wave impedance determination for the sequence of not only constant potentials but also for potentials of forms for which the solution of a Shr\"{o}dinger equation exists at least in terms of…

We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…

This paper proposes a numerical method for solving time-dependent Schrodinger equations with finite spectral bandwidth, which applies to both periodic and non-periodic cases. We introduce the concept of Pulse Width Modulation (PWM), which…

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including…

Suzuki-Trotter decomposition is a well-known technique used to calculate the partition function of quantum spin systems, in which the imaginary-time dependence of the partition function occurs inevitably. Since it is very difficult to…

Simulating quantum many-body dynamics is important both for fundamental understanding of physics and practical applications for quantum information processing. Therefore, classical simulation methods have been developed so far.…

We develop a stable and efficient numerical scheme for modeling the optical field evolution in a nonlinear dispersive cavity with counter propagating waves and complex, semiconductor physics gain dynamics that are expensive to evaluate. Our…

The Helmholtz equation is a prototypical model for time-harmonic wave propagation. Numerical solutions become increasingly challenging as the wave number $k$ grows, due to the equation's elliptic yet noncoercive character and the highly…

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining…

We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a…

We present quantum algorithms for simulating the dynamics of a broad class of classical oscillator systems containing $2^n$ coupled oscillators (Eg: $2^n$ masses coupled by springs), including those with time-dependent forces, time-varying…