Related papers: A stable semi-implicit algorithm
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
Semi-implicit spectral deferred correction (SDC) methods provide a systematic approach to construct time integration methods of arbitrarily high order for nonlinear evolution equations including conservation laws. They converge towards $A$-…
This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…
We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn-Hilliard models with variable mobility. This splitting method…
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…
The concept of evolutionarily stability and its relation with the fixed points of the replicator equation are important aspects of evolutionary game dynamics. In the light of the fact that oscillating state of a population and individuals…
The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. We study operator-algebraic forms of stability for unitary representations of groups and…
In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…
We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is…
In this paper we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of…
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity…
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…
Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers. These solvers are computationally expensive, requiring the use of tiny step sizes for numerical stability and…
Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in…
This paper presents a new type of genetic algorithm for the set covering problem. It differs from previous evolutionary approaches first because it is an indirect algorithm, i.e. the actual solutions are found by an external decoder…
We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
This paper examines small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We show that the mere existence of a high-voltage power flow solution does not necessarily imply small-signal…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…