Related papers: Functional-preserving predictor-corrector multider…
Training Neural ODEs requires backpropagating through an ODE solve. The state-of-the-art backpropagation method is recursive checkpointing that balances recomputation with memory cost. Here, we introduce a class of algebraically reversible…
Spectral deferred correction (SDC) methods are an attractive approach to iteratively computing collocation solutions to an ODE by performing so-called sweeps with a low-order time stepping method. SDC allows to easily construct high order…
We introduce and analyze a family of heterogeneous multiscale methods for the numerical integration of highly oscillatory systems of delay differential equations with constant delays. The methodology suggested provides algorithms of…
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…
When dealing with stiff conservation laws, explicit time integration forces to employ very small time steps, due to the restrictive CFL stability condition. Implicit methods offer an alternative, yielding the possibility to choose the time…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…
A higher-order numerical method is presented for scalar valued, coupled forward-backward stochastic differential equations. Unlike most classical references, the forward component is not only discretized by an Euler-Maruyama approximation…
We introduce a multigrid multilevel Monte Carlo method for stochastic trace estimation in lattice QCD based on orthogonal projections. This formulation extends the previously proposed oblique decomposition and it is assessed on three…
We introduce a new class of arbitrary-order exponential time differencing methods based on spectral deferred correction (ETDSDC) and describe a simple procedure for initializing the requisite matrix functions. We compare the stability and…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular…
This paper proposes a new class of mass or energy conservative numerical schemes for the generalized Benjamin-Ono (BO) equation on the whole real line with arbitrarily high-order accuracy in time. The spatial discretization is achieved by…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We are concerned in designing a suitable numerical scheme based on the equal-order hybrid high-order (HHO) method for the linear parabolic integro-differential equations. The spatial discretization is made using the equal-order HHO method…
We are interested in the numerical approximation of non-linear stochastic differential equations (SDEs) with solution in a certain domain. Our goal is to construct explicit numerical schemes that preserve that structure. We generalize the…
The problem of recovering partial derivatives of high orders of bivariate functions with finite smoothness is studied. Based on the truncation method, a numerical differentiation algorithm was constructed, which is optimal by the order,…
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.
High order strong stability preserving (SSP) time discretizations are often needed to ensure the nonlinear (and sometimes non-inner-product) strong stability properties of spatial discretizations specially designed for the solution of…