Related papers: Tchebychev Polynomial Approximations for $m^{th}$ …
In this paper, we study a class of boundary value problems (BVPs) with Robin conditions in some $L^p$ spaces for polyharmonic equation on Lipschitz domains. Utilizing polyharmonic fundamental solutions, these Robin BVPs are solved by the…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
The paper considers a boundary value problem for the high-order Lavrent'ev-Bitsadze equation. Necessary and sufficient conditions for the uniqueness of the solution are found. When substantiating the existence, the problem of "small…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…
In this paper, an efficient method is presented for solving three dimensional Volterra integral equations of the second kind with continuous kernel. Shifted Chebyshev polynomial is applied to approximate a solution for these integral…
In this paper we propose an adaptive scheme for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel-based method of lines that allows us to split the spatial and time…
We investigate the problem of numerical differentiation of bivariate functions from weighted Wiener classes using Chebyshev polynomial expansions. We develop and analyze a new version of the truncation method based on Chebyshev polynomials…
In this paper, we propose a neural network learning algorithm for solving eigenvalue problems and boundary value problems (BVPs) for elliptic operators and initial BVPs (IBVPs) of quasi-linear parabolic equations in high dimensions as well…
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
This paper presents for the first time a robust exact line-search method based on a full pseudospectral (PS) numerical scheme employing orthogonal polynomials. The proposed method takes on an adaptive search procedure and combines the…
This paper discusses the initial-boundary-value problems (IBVP) of nonlinear Schr\"odinger equations posed in a half plane $\mathbb{R} \times \mathbb{R}^+$ with nonhomogeneous Dirichlet boundary conditions. For any given $s \ge 0$, if the…
We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems.…
Mixed level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao and Gilbert-Varshamov type bounds for mixed level orthogonal arrays. The computational complexity of the terms involved…
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…
In this article we prove solvability results for $L^2$ boundary value problems of some elliptic systems $Lu=0$ on the upper half-space $\R^{n+1}_{+}, n\ge 1$, with transversally independent coefficients. We use the first order formalism…
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 design high order accurate and stable finite difference schemes for the initial-boundary value problem, associated with the magnetic induction equation with resistivity. We use Summation-By-Parts (SBP) finite difference…
We consider an approximate solution for the one-dimensional semilinear singularly-perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of…