Related papers: Two Quantum Algorithms for Nonlinear Reaction-Diff…
We present a mapping of the nonlinear, electrostatic Vlasov equation with Krook-type collision operators, discretized on a (1+1) dimensional grid, onto a recent Carleman linearization-based quantum algorithm for solving ordinary…
A novel second order family of explicit stabilized Runge-Kutta-Chebyshev methods for advection-diffusion-reaction equations is introduced. The new methods outperform existing schemes for relatively high Peclet number due to their favorable…
The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation,…
In this study, the numerical solutions of reaction-diffusion systems are investigated via the trigonometric quintic B-spline nite element collocation method. These equations appear in various disciplines in order to describe certain…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in $\mathbb{R}^n$. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
We present a method for solving the reaction-diffusion equation with general potential in free space. It is based on the approximation of the Feynman-Kac formula by a sequence of convolutions on sequentially diminishing grids. For…
Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of…
The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To apply the HHL to non-linear problems such as chemical reactions, the system must…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
We explore the class of exponential integrators known as exponential time differencing (ETD) method in this letter to design low complexity nonlinear Fourier transform (NFT) algorithms that compute discrete approximations of the scattering…
Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
We present the Fast Chebyshev Transform (FCT), a fast, randomized algorithm to compute a Chebyshev approximation of functions in high-dimensions from the knowledge of the location of its nonzero Chebyshev coefficients. Rather than sampling…