相关论文: On the solutions of generalized discrete Poisson e…

This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and…

We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is…

This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Fourier Singular Complement Method is introduced and analysed,…

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

An improved finite difference method with compact correction term is proposed to solve the Poisson equations. The compact correction term is developed by a coupled high-order compact and low-order classical finite difference formulations.…

The solution of Poisson's equation plays a key role in constructing the martingale through which sums of Markov correlated random variables can be analyzed. In this paper, we study two different representations for the solution in countable…

We consider the Goursat problem for linear partial differential equations with constant coefficients in two complex variables. We find the conditions for summable solutions of the Goursat problem in the case when the Newton polygon has…

We give a constructive approach for the study of integral representations of classical solutions to Poisson equations under some integrability conditions on data functions.

We derive special forms of the Poisson summation formula for even and odd functions, which are applied to obtain representations for Euler-type numbers and to sum various series related to elliptic functions.

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

I begin from a particular field of generalised Puiseux series and investigate a class of nonlinear differential equations in the field. It is appeared that the main part of differential equation determines solvability and positions of…

We introduce a new type of recurrence in the space of continuous and bounded functions. The property is easily verifiable, and can be considered for differential equations. This time, the existence and asymptotic stability of modulo…

We give a simple proof of the fact that there exist measures on the real line of discrete support, whose Fourier Transform is also a measure of discrete support, yet this Fourier pair cannot be constructed by repeatedly applying the Poisson…

We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When…

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

We prove that a Poisson-Newton formula, in a broad sense, is associated to each Dirichlet series with a meromorphic extension to the whole complex plane. These formulas simultaneously generalize the classical Poisson formula and Newton…

Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…

In this paper we explain how to use the Fast Fourier Transform (FFT) to solve partial differential equations (PDEs). We start by defining appropriate discrete domains in coordinate and frequency domains. Then describe the main limitation of…

In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…