Related papers: Partial differential equations from integrable ver…
We consider quantum integrable models solvable by the algebraic Bethe ansatz and possessing $\mathfrak{gl}(2)$-invariant $R$-matrix. We study the models of both periodic boundary conditions and boundary conditions based on reflection…
The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It…
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
We introduce a layer potential representation for the solution of the transmission problem defined by two dielectric channels, or open wave-guides, meeting along the straight-line interface, $\{x_1=0\}.$ The main observation is that the…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of corresponding three-dimensional lattice models. We present the modified version of these equations which give the…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
In this paper we presents an algorithm for finding a solution of the linear nonhomogeneous quaternionic-valued differential equations. Moveover, several examples shows the feasibility of our algorithm.
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and…
Fuzzy partial integro-differential equations have a major role in the fields of science and engineering. In this paper, we propose the solution of fuzzy partial Volterra integro-differential equation with convolution type kernel using fuzzy…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible…
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…