Related papers: Construction of Laguerre pseudospectral differenti…
A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential…
We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogenisation, or for fitting Laguerre diagrams to EBSD or XRD…
We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong…
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
Discrete orthogonal matrices have several applications in information technology, such as in coding and cryptography. It is often challenging to generate discrete orthogonal matrices. A common approach widely in use is to discretize…
The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…
Pseudospectral methods represent an efficient approach for solving optimal control problems. While Legendre-Gauss-Lobatto (LGL) collocation points have traditionally been considered inferior to Legendre-Gauss (LG) and Legendre-Gauss-Radau…
Variance reduction is a crucial idea for Monte Carlo simulation and the stochastic Lanczos quadrature method is a dedicated method to approximate the trace of a matrix function. Inspired by their advantages, we combine these two techniques…
The finite Laguerre transform is applied to solve Differential Equations Problems of order higher than two and a one-dimensional steady-state Schr\"{o}dinger equation, by using elementary Linear Algebra methods.
In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series. In addition some of…
The Sobolev-Laguerre polynomials form an orthogonal polynomial system with respect to a Sobolev-type inner product associated with the Laguerre measure on the positive half-axis and two point masses $M,N > 0$ at the origin involving…
The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
In the present note we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs): from one side they could look standard, since they are, real, symmetric…
Laguerre tessellations of macromolecules capture properties such as molecular interface surfaces, volumes and cavities. Explicit solvent molecular dynamics simulations of a macromolecule are slow as the number of solvent atoms considered…
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…
Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and…
A series of problems in different fields such as physics and chemistry are modeled by differential equations. Differential equations are divided into partial differential equations and ordinary differential equations which can be linear or…