Related papers: Methods for solution of boundary value problems in…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
In the present article we present a particular combination of boundary problems for the inhomogeneous tri-analytic equation: the Neumann-(Dirichlet-Neuman) problem and the (Dirichlet-Neumann)-Dirichlet problem. In order to obtain the…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
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…
A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. Boundary-domain integral equations are…
In this paper, we discuss differentiation of solutions to the boundary value problem $y^{(n)} = f(x, y, y^{'}, y^{''}, \ldots, y^{(n-1)}), \; a<x<b,\; y^{(i)}(x_j) = y_{ij},\; 0\leq i \leq m_j, \; 1 \leq j \leq k-1$, and $y^{(i)}(x_k) +…
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the…
We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem…
In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly-anisotropic diffusion problems. In particular, we analyze the performances of different approaches which are…
We investigate the existence and multiplicity of solutions for higher order discrete boundary value problems via critical point theory.
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…
We present a new view onto the successive approximations' approach in study of the two-point nonlinear fractional boundary value problems. In order to reduce the original problem and further construct its approximate solution we use the…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face $x=0$, variable in time, is considered. Throught several transformations the problem is reduced to a free…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
This paper is concerned with problems of scattering of time-harmonic acoustic waves by a two-layered medium with a non-locally perturbed boundary (called a rough boundary in this paper) in two dimensions, where a Dirichlet or impedance…
We investigate the existence and multiplicity of solutions for fourth order discrete boundary value problems via critical point theory.
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These…
We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…