Related papers: Fully pseudospectral time evolution and its applic…
A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schrodinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) method, the fast Fourier transform is used to…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite…
The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equations (SPDEs) defined on the whole space. Sufficient conditions…
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
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 this paper, we present a novel pseudospectral (PS) method for solving a new class of initial-value problems (IVPs) of time-dependent one-dimensional fractional partial differential equations (FPDEs) with variable coefficients and…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
A nonstationary spherically symmetric problem for conformal geometrodynamics equations is considered and general exact solutions in quadratures are obtained. Involvement of Weyl degrees of freedom allows us to consider the problem with…
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 paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
We introduce a single patch collocation method in order to compute solutions of initial value problems of partial differential equations whose spatial domains are 3-spheres. Besides the main ideas, we discuss issues related to our…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
Recently, the numerical solution of multi-frequency, highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in time. When the problem derives from the space semi-…
In this paper, we describe in detail a scheme for the construction of highly accurate numerical solutions to Einstein's field equations in five and six spacetime dimensions corresponding to non-uniform black strings. The scheme consists of…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We derive the evolution equations for the spectra of the Universe. Here "spectra" means the eigenvalues of the Laplacian defined on a space, which contain the geometrical information on the space. These equations are expected to be useful…
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary…