Related papers: Numerical Solution of the Boundary Value Problems …
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems(FN-BVPs) with Robin Boundary Conditions(RBCs). In the new numerical schemes, a two-point FNBVP is transformed into a system of…
Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. Especially, Neumann and Robin BVPs are considered. The main obstacle for applying the usual…
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
Providing fast and accurate solutions to partial differential equations is a problem of continuous interest to the fields of applied mathematics and physics. With the recent advances in machine learning, the adoption learning techniques in…
In the presented work, we solve the Dirichlet boundary problem for the Helmholtz equation in an exterior angle with periodic boundary data. We prove the existence and uniqueness of solution in an appropriate funcional class and we give an…
The purpose of the present research is to investigate model mixed boundary value problems for the Helmholtz equation in a planar angular domain $\Omega_\alpha\subset\mathbb{R}^2$ of magnitude $\alpha$. The BVP is considered in a…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…
In this paper we propose a Local Orthogonal Decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet- and Neumann boundary conditions. For this purpose, we present new boundary correctors which…
In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
In recent years, partial differential equation (PDE) systems have been successfully applied to the binarization of text images, achieving promising results. Inspired by the DH model and incorporating a novel image modeling approach, this…
In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition as well as the state in the Neumann boundary value problem for an elliptic partial differential…
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the…
In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of…