Related papers: An iterative approximate method of solving boundar…
We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
In this paper we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
We prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed point index. Some of the…
The inversion problem for rational B\'ezier curves is addressed by using resultant matrices for polynomials expressed in the Bernstein basis. The aim of the work is not to construct an inversion formula but finding the corresponding value…
We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current…
The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix A of the overdetermined system to be solved in the least squares sense is then a rectangular…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimates,~and then proceed to the discrete setting.~We formulate…
Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation,…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using seventh degree B-Spline function. Formulation is based on particular terms of order of seventh order…
We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…
In a rectangular domain, a boundary-value problem is considered for a mixed-type equation with a regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's fractional derivative. Using the method…
We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schr\"odinger equation. We approximate the solution using a, local (non-uniform) two level scheme in time (see C. Besse [6]…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
In a multidimensional infinite layer bounded by two hyperplanes, the inhomogeneous Helmholtz equation with a polynomial right-hand side is considered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-value problems with…