Related papers: Fractional calculus via variable-transform-based s…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of…
In this work the spectral theory of self-adjoint operator $A$ represented by Jacobi matrix is considered. The approach is based on the continued fraction representation of the resolvent matrix element of $A$. Different criteria of absolute…
We present a spectral scheme for atomic structure calculations in pseudopotential Kohn-Sham density functional theory. In particular, after applying an exponential transformation of the radial coordinates, we employ global polynomial…
A framework for Chebyshev spectral collocation methods for the numerical solution of functional and delay differential equations (FDEs and DDEs) is described. The framework combines interpolation via the barycentric resampling matrix with a…
This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper in J.…
Numerical approximation of the Boltzmann equation presents a challenging problem due to its high-dimensional, nonlinear, and nonlocal collision operator. Among the deterministic methods, the Fourier-Galerkin spectral method stands out for…
We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. We use the arc-length representation of the differential…
Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to…
We explore the class of exponential integrators known as exponential time differencing (ETD) method in this letter to design low complexity nonlinear Fourier transform (NFT) algorithms that compute discrete approximations of the scattering…
Causal parametric representations of neutron-star equations of state are constructed here using Chebyshev polynomial based spectral expansions. The accuracies of these representations are evaluated for a collection of model equations of…
The aim of the present work is to introduce a method based on Chebyshev polynomials for the numerical solution of a system of Cauchy type singular integral equations of the first kind on a finite segment. Moreover, an estimation error is…
We investigate the variable-exponent Abel integral equations and corresponding fractional Cauchy problems. The main contributions of the work are enumerated as follows: (i) We develop an approximate inversion technique for variable-exponent…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We consider radially symmetric capillary surfaces that are described by bounded generating curves. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points…