Related papers: On one method of boundary value problem regulariza…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
For a given level of accuracy in option prices, the paper considers the problem of deciding when exactly, as one or more of the pricing parameters change, a barrier option degenerates into a simpler type of option. This problem is…
We study the most general class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the complex H\"older space $C^{n+r,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…
The existence of numerical solutions to a fourth order singular boundary value problem arising in the theory of epitaxial growth is studied. An iterative numerical method is applied on a second order nonlinear singular boundary value…
Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…
An initial-value problem for an ordinary differential equation of the first order, is considered. It is supposed that the right-hand side of the equation is a continuous function defined on a set consisting of an open set and a part of its…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
We present here a review of existing analytical methods to solve boundary value problems of diffusion in media containing N non-overlapping inclusions.
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…
We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
In this paper the simplest singular boundary problem of Dirichlet type for linear differential equation of the first order of general form is considered. The main result of this paper is criterion of correct solvability of above problem in…