Related papers: A pseudo-spectral approach to constructing rotatin…
A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi…
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…
Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the…
To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is…
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…
We show the existence of a new class of initially smooth spherically symmetric self-similar solutions to the non-isentropic Euler-Poisson system. These solutions exhibit supersonic gravitational implosion in the sense that the density…
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for…
It has been shown that scalar fields can form gravitationally bound compact objects called boson stars. In this study, we analyze boson star configurations where the scalar fields contain a small amount of angular momentum and find two new…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
In this article, we combine the periodic sinc basis set with a curvilinear coordinate system for electronic structure calculations. This extension allows for variable resolution across the computational domain, with higher resolution close…
In this paper, we introduce a numerical solution of a stochastic partial differential equation (SPDE) of elliptic type using polynomial chaos along side with polynomial approximation at Sinc points. These Sinc points are defined by a…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
We study the spontaneous scalarization of spherically symmetric, asymptotically flat boson stars in the $(\alpha {\cal R} + \gamma {\cal G}) \phi^2$ scalar-tensor gravity model. These compact objects are made of a complex valued scalar…
We consider axially symmetric, rotating boson stars. Their flat space limits represent spinning Q-balls. We discuss their properties and determine their domain of existence. Q-balls and boson stars are stationary solutions and exist only in…
The Einstein field equations, or generalizations thereof, are difficult to solve analytically. On the other hand, numerical solutions of the same equations have become increasingly common, in particular concerning compact objects. Whereas…
We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…
We present a mathematically rigorous quantum-mechanical treatment of a two-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb like potentials) on pseudosphere and compare their spectra and the sets of…