Related papers: Setup of Order Conditions for Splitting Methods
We investigate the equivalence of different operator-splitting schemes for the integration of the Langevin equation. We consider a specific problem, so called the directed percolation process, which can be extended to a wider class of…
We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…
In this work, we propose a Proper Orthogonal Decomposition-Reduced Order Model (POD-ROM) applied to time-splitting schemes for solving the Navier-Stokes equations with open boundary conditions. In this method, we combine three strategies to…
Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the…
In this article, the operator approach to modeling numeral systems is introduced. This approach can be useful for coding information and providing computer protection. Certain examples of such numeral systems are considered. In addition,…
We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell's equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…
We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it…
We give an outline of a formalism for the solution of the evolution equations for off-forward parton distributions in leading and next-to-leading orders based on partial conformal wave expansion and orthogonal polynomials reconstruction.
This paper presents an efficient strategy for constructing Reduced-Order Model (ROM) bases using Taylor polynomial expansions and Fr{\'e}chet derivatives with respect to model parameters. The proposed approach enables the construction of…
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be solved efficiently and accurately. Traditionally, these…
The current implementation of Thiele rational interpolation in Maple (the ThieleInterpolation routine) breaks down when the points are not well-ordered. In this article, it is shown how this breakdown can be avoided by ordering the…
The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
A Lax operator algebra is constructed for an arbitrary semi-simple Lie algebra over $\mathbb C$ equipped with a $\mathbb Z$-grading, and arbitrary compact Riemann surface with marked points. In this set-up, a treatment of almost graded…
In this paper we consider a logical treatment for the ordered disjunction operator 'x' introduced by Brewka, Niemel\"a and Syrj\"anen in their Logic Programs with Ordered Disjunctions (LPOD). LPODs are used to represent preferences in logic…
This paper describes an algorithm for the compilation of a two (or more) level orthographic or phonological rule notation into finite state transducers. The notation is an alternative to the standard one deriving from Koskenniemi's work: it…
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…
Some more general "inheritance conditions" have been found for a given set of symmetry generators $\{\mathbf{Z}_{\bar{l}}\}$ acting on some set of coupled ordinary differential equations, once the "first integration method" has been applied…