Related papers: An Iterative Transformation Method for a Similarit…
We propose an iterative method for nonlinear semidefinite programs with box constraints. The search direction in the proposed method utilizes the distance from the current point to the boundary of a feasible set. The computation of the…
We numerically implement the variational approach for reconstruction in the inverse crack and cavity problems developed by one of the authors. The method is based on a suitably adapted free-discontinuity problem. Its main features are the…
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…
In this paper we propose the design of an iterative observer using space as a time-like variable and prove its convergence. The iterative observer algorithm solves boundary estimation problem for a steady-state elliptic equation system…
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation…
A theoretical analysis of the finite element method for a generalized Robin boundary value problem, which involves a second-order differential operator on the boundary, is presented. If $\Omega$ is a general smooth domain with a curved…
The paper deals with a boundary value problem for the nonlinear integro-differential equation $u^{\prime\prime\prime\prime}-m\left(\int_0^l {u^\prime}^2dx\right)u^{\prime\prime}=f(x,u,u^\prime), \; m(z)\geq \alpha>0, \; 0\leq z <\infty$,…
A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is…
This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…
We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…
We present here a review of existing analytical methods to solve boundary value problems of diffusion in media containing N non-overlapping inclusions.
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method…
This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of…
We consider four definitions of solution to the initial-boundary value problem for a scalar balance laws in several space dimensions. These definitions are generalised to the same most general framework and then compared. The first aim of…
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense…
We present an interval-based approach for parameter identification in structural static inverse problems. The proposed inverse formulation exploits the Interval Finite Element Method (IFEM) combined with adjoint-based optimization. The…
This article proposes a hybrid adaptive numerical method based on the Dual Reciprocity Method (DRM) to solve problems with non-linear boundary conditions and large-scale problems, named Hybrid Adaptive Dual Reciprocity Method (H-DRM). The…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…