相关论文: Another universal differential equation

Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building…

A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.

A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of finite-gap integration. The parametrisation of the solutions…

Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its…

The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.

Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…

The problem of differentiating a function with bounded second derivative in the presence of bounded measurement noise is considered in both continuous-time and sampled-data settings. Fundamental performance limitations of causal…

A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of…

This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…

We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a…

We present \textit{universal} estimators for the statistical mean, variance, and scale (in particular, the interquartile range) under pure differential privacy. These estimators are universal in the sense that they work on an arbitrary,…

A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…

Opial's inequality and its ramifications play an important role in the theory of differential and difference equations. A sharp unifying generalization of Opial's inequality is presented that contains both its continuous and discrete…

In solving diffusion problems, it is common to consider the finite difference equation to be an approximation to the differential equation. Nevertheless, history shows that the finite difference equation is primitive and that the…

This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…

The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are…

We use the jump problem technique developed in a recent paper by Grushevsky, Krichever and the second author to compute the variational formula of any stable differential and its periods to arbitrary precision in plumbing coordinates. In…

We begin by introducing the main ideas of the paper under discussion, and we give a brief description of the method proposed. Next, we discuss an alternative approach based on B-spline expansion, and lastly we make some comments on the…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

This is not a new result. Purpose of this work is to describe a method to search the analytical expression of the general real solution of the two-dimensional Laplace differential equation. This thing is not easy to find in scientific…