Related papers: Inverse Inequality Estimates with Symbolic Computa…
A variation of Zeilberger's holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original…
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
We consider fourth order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the $h$ version of the Finite Element Method (FEM). In particular, we use piecewise Hermite polynomials of degree…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
In latest years, several advancements have been made in symbolic-numerical eigenvalue techniques for solving polynomial systems. In this article, we add to this list. We design an algorithm which solves systems with isolated solutions…
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
We present broadly applicable tools for determining the behavior of eigenvalues and eigenvectors under the addition of self-adjoint operators and under the multiplication of unitaries, in finite-dimensional Hilbert spaces. The new tools…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
In this work, we analyze the finite element method with arbitrary but fixed polynomial degree for the nonlinear Helmholtz equation with impedance boundary conditions. We show well-posedness and error estimates of the finite element solution…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
We discuss the $p$- and the $hp$-versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schr\"odinger…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…