Related papers: An Integral Equation Method for Linear Two-Point B…
We present a high order numerical method for the solution of the Neumann Green's function in two dimensions. For a general closed planar curve, our computational method resolves both the interior and exterior Green's functions with the…
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+\lambda…
In this short note, we present the sharp estimate for the existence of a unique solution for a Hadamard-type fractional differential equations with two-point boundary value conditions. The method of analysis is obtained by using 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…
Traditional boundary integral methods suffer from the singularity of Green's kernels. The paper develops, for a model problem of 2D scattering as an illustrative example, singularity-free boundary difference equations. Instead of converting…
This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…
This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…
The authors propose a Nystrom method to approximate the solution of a boundary integral equation connected with the exterior Neumann problem for Laplace's equation on planar domains with corners. They prove the convergence and the stability…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii's fixed point theorem on cones, sufficient conditions for the…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
The authors consider the interior Dirichlet problem for Laplace's equation on planar domains with corners. In order to approximate the solution of the corresponding double layer boundary integral equation, they propose a numerical method of…
We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation.…
We revisit the volume Green's function integral equation for modelling light scattering with discretization strategies as well as numerical integration recipes borrowed from finite element method. The merits of introducing finite element…
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…
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 focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
An algorithm for the direct inversion of the linear systems arising from Nystrom discretization of integral equations on one-dimensional domains is described. The method typically has O(N) complexity when applied to boundary integral…