Related papers: A direct PinT algorithm for higher-order nonlinear…
As has been shown in our previous work, the parallel-in-time direct inverse (ParaDIn) method introduced by Yamaleev and Paudel in (arXiv: 2406.00878v1, 2024) imposes some constraint on the maximum number of time levels, $N_t$, that can be…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially non-oscillatory (WENO)…
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…
We solve numerically to order 1/N the time evolution of a quantum dynamical system of N oscillators of mass m coupled quadratically to a massless dynamic variable. We use Schwinger's closed time path (CTP) formalism to derive the equations.…
High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a…
With the advent of supercomputers, multi-processor environments and parallel-in-time (PinT) algorithms offer ways to solve initial value problems for ordinary and partial differential equations (ODEs and PDEs) over long time intervals, a…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
For the iterative decoupling of elliptic-parabolic problems such as poroelasticity, we introduce time discretization schemes up to order $5$ based on the backward differentiation formulae. Its analysis combines techniques known from…
We propose a third order dynamical system for solving a nonlinear equation in Hilbert spaces where the operator is cocoercive with respect to the solutions set. Under mild conditions on the parameters, we establish the existence and…
Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a variational approach, we employ a finite difference…
This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
We introduce Prob-GParareal, a probabilistic extension of the GParareal algorithm designed to provide uncertainty quantification for the Parallel-in-Time (PinT) solution of (ordinary and partial) differential equations (ODEs, PDEs). The…
The aim of this paper is to develop and analyze high-order time stepping schemes for solving semilinear subdiffusion equations. We apply the $k$-step BDF convolution quadrature to discretize the time-fractional derivative with order…