Related papers: Optimizing the Evolution of Perturbations in the $…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
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…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
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…
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…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and…
The Chebyshev expansion method is a well-established technique for computing the time evolution of quantum states, particularly in Hermitian systems with a bounded spectrum. Here, we show that the applicability of the Chebyshev expansion…
By means of the present geometrical and dynamical observational data, it is very hard to establish, from a statistical perspective, a clear preference among the vast majority of the proposed models for the dynamical dark energy and/or…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
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 derive the full set of second-order equations governing the evolution of cosmological perturbations, including the effects of the first-order electron number density perturbations, \delta_e. We provide a detailed analysis of the…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
We study inhomogeneous perturbations away from the strongly homogeneous background cosmology previously studied. The problem is greatly simplified by using the mapping on the inner Schwarzschild solution. The resulting linear perturbation…
The observational success and simplicity of the $\Lambda$CDM model, and the explicit analytic perturbations thereof, set the standard for any alternative cosmology. It therefore serves as a comparison ground and as a test case for methods…
We investigate deviations from $\Lambda$CDM by independently parameterizing modifications in the background evolution and the growth of structures. The background is characterized by two parameters, $A$ and $B$, which reduce to…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
A new and promising avenue was recently developed for analyzing large-scale structure data with a model-independent approach, in which the linear power spectrum shape is parametrized with a large number of freely varying wavebands rather…
Perturbation Theory to Large Scale Structure Cosmology proposes corrections to the linearly evolved density contrast and velocity in terms of a series development in which all terms are integrals of powers of the linear density contrast…
Creation of Cold Dark Matter (CCDM) can macroscopically be described by a negative pressure, and, therefore, the mechanism is capable to accelerate the Universe, without the need of an additional dark energy component. In this framework we…