Related papers: Spectral methods in general relativistic astrophys…
As a continuation of our previous work \cite{KV2} the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces…
We construct global-in-time solutions for semilinear parabolic rough partial differential equations. We work on a scale of Banach spaces tailored to the controlled rough path approach and derive suitable a-priori estimates of the solution…
Kadath is a library that implements spectral methods in a very modular manner. It is designed to solve a wide class of problems that arise in the context of theoretical physics. Several types of coordinates are implemented and additional…
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…
We compute spectra from accretion disks around rapidly rotating neutron stars. The full effect of general relativity is considered for the structure calculation of the stars. We take into account the Doppler shift, gravitational redshift…
In this paper, we propose some algorithms for analytical solution construction to nonlinear polynomial partial differential equations with constant function coefficients. These schemes are based on one-(single), two- (double) or three-…
We present a version of the conditional symmetry method in order to obtain multiple wave solutions expressed in terms of Riemann invariants. We construct an abelian distribution of vector fields which are symmetries of the original system…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
We develop an algebraic method of studying of Diophantine quadratic equations in three variables over the ring of Gaussian integers.
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…
We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
We propose a numerical method to solve the three-dimensional static Maxwell equations in a singular axisymmetric domain, generated by the rotation of a singular polygon around one of its sides. The mathematical tools and an in-depth study…
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…