相关论文: Rational Chebyshev Spectral Transform for the dyna…
In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of $O(N_{\text{iter.}}N\log…
Reaction-Diffusion equations can present solutions in the form of traveling waves. Such solutions evolve in different spatial and temporal scales and it is desired to construct numerical methods that can adopt a spatial refinement at…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of $T=0$ many-body spectral functions to a much higher precision by deriving a modified…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
We present a numerical spectral method to solve systems of differential equations on an infinite interval $y\in (-\infty, \infty)$ in presence of linear differential operators of the form $Q(y) \left(\partial/\partial_y\right)^b$ (where…
This paper presents a novel approach to rigorously solving initial value problems for semilinear parabolic partial differential equations (PDEs) using fully spectral Fourier-Chebyshev expansions. By reformulating the PDE as a system of…
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…
Peridynamics is a nonlocal generalization of continuum mechanics theory which adresses discontinuous problems without using partial derivatives and replacing its by an integral operator. As a consequence, it finds applications in the…
Unions of graph Fourier multipliers 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 to the high-dimensional signals…
Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored. This paper aims at developing accurate…
Analytic expressions for the Fourier transforms of the Chebyshev and Legendre polynomials are derived, and the latter is used to find a new representation for the half-order Bessel functions. The numerical implementation of the so-called…
Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…
We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is…
We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical…
In the above paper the author treats the boundary layer flow of an electrically conducting, non-Newtonian fluid along a vertical plate embedded in a Darcy-Brinkman-Forchheimer porous medium. The fluid is under the action of a constant…
This paper is focused on performing a new method for solving linear and nonlinear higher-order boundary value problems (HBVPs). This direct numerical method based on spectral method. The trial function of this method is the Monic Chebyshev…
Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian…
A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands…
Numerical simulation of superconducting devices is a powerful tool for understanding the principles of their work and improving their design. We present a new pseudospectral method for two-dimensional magnetization and transport current…