Related papers: Operator-splitting schemes for degenerate, non-loc…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
In this paper we present a non-local numerical scheme based on the Local Discontinuous Galerkin method for a non-local diffusive partial differential equation with application to traffic flow. In this model, the velocity is determined by…
This article is devoted to the construction of new numerical methods for the semiclassical Schr\"odinger equation. A phase-amplitude reformulation of the equation is described where the Planck constant epsilon is not a singular parameter.…
The multi-scale and non-linear nature of phase-field models of solidification requires fine spatial and temporal discretization, leading to long computation times. This could be overcome with artificial-intelligence approaches. Surrogate…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
Solving Stefan problems via neural networks is inherently challenged by the nonlinear coupling between the solutions and the free boundary, which results in a non-convex optimization problem. To address this, this work proposes an Operator…
A conservative discontinuous Galerkin scheme for a nonlinear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it…
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid…
Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
First, using the uniform decomposition in both physical and frequency spaces, we obtain an equivalent norm on modulation spaces. Secondly, we consider the Cauchy problem for the dissipative evolutionary pseudo-differential equation…
We propose a short-memory operator splitting scheme for solving the constant-Q wave equation, where the fractional stress-strain relation contains multiple Caputo fractional derivatives with order much smaller than 1. The key is to exploit…
We present two semidiscretizations of the Camassa-Holm equation in periodic domains based on variational formulations and energy conservation. The first is a periodic version of an existing conservative multipeakon method on the real line,…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
We discuss a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…
On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The…
This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical…
Variable division and optimization (D\&O) is a frequently utilized algorithm design paradigm in Evolutionary Algorithms (EAs). A D\&O EA divides a variable into partial variables and then optimize them respectively. A complicated problem is…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…