Related papers: Setup of Order Conditions for Splitting Methods
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
The normal form theorem, proved in R. Laver, On the left distributive law and the freeness of an algebra of elementary embeddings, Advances in Mathematics 91 (1992), 209-231, for the free algebra $\Cal A$ on one generator $x$ satisfying the…
This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
We show that the Bellman operator underlying the options framework leads to a matrix splitting, an approach traditionally used to speed up convergence of iterative solvers for large linear systems of equations. Based on standard comparison…
Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form $\dot{x} = f_0(x) + f_1(x)$, where $f_0$ encodes non-reversible dynamics, motivating schemes…
Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a…
The notions of expansivity and positive expansivity for composition operators on Orlicz spaces are investigated. In particular, necessary and sufficient conditions are given for a composition operator to be expansive, positively expansive,…
The use of operator-splitting methods to solve differential equations is widespread, but the methods are generally only defined for a given number of operators, most commonly two. Most operator-splitting methods are not generalizable to…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be denoted by $p$ in the…
We consider a simple model of higher order, functional computation over the booleans. Then, we enrich the model in order to encompass non-termination and unrecoverable errors, taken separately or jointly. We show that the models so defined…
This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods for obtaining Lie algebras of conditional symmetries from…
A systematic algorithm for building integrating factors of the form mu(x,y), mu(x,y') or mu(y,y') for second order ODEs is presented. The algorithm can determine the existence and explicit form of the integrating factors themselves without…
We show how the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics (with accuracy of order $\tau^2$ for a timestep of length $\tau$) can be improved in a systematic manner without using the…
We consider a higher-order Milstein scheme for stochastic partial differential equations with trace class noise which fulfill a certain commutativity condition. A novel technique to generally improve the order of convergence of Taylor…
This paper describes a system, called PLP, for compiling ordered logic programs into standard logic programs under the answer set semantics. In an ordered logic program, rules are named by unique terms, and preferences among rules are given…