Related papers: On the initial value problem of a periodic box-bal…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at…
Mathematical formula describing the periodicity of the elements in the periodic system is presented.
We consider first-order linear systems of ordinary differential equations with periodic coefficients. Supposing that right-hand sides of equations are not known and subjected to some quadratic restrictions, we obtain optimal, in certain…
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in classes of regular solutions in the cases of…
This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
This study proposes an approach toward the first principles electronic structure calculation with the aid of symbolic-numeric solving. The symbolic computation enables us to express the Hartree-Fock-Roothaan equation and the molecular…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
We consider the abstract initial value problem for the system of evolution equations which describe motion of micropolar fluids with heat conduction in a bounded domain. This problem has uniquely a mild solution locally in time for general…
A technique is described in this paper to avoid order reduction when integrating reaction-diffusion initial boundary value problems with explicit exponential Rosenbrock methods. The technique is valid for any Rosenbrock method, without…
Spacetime is foliated by spatial hypersurfaces in the 3+1 split of General Relativity. The initial value problem then consists of specifying initial data for all relevant fields on one such a spatial hypersurface. These fields are the…
In a 1979 paper, K. Okamoto introduced the space of initial values for the six Painlev\'e equations and their associated Hamiltonian systems, showing that these define regular initial value problems at every point of an augmented phase…
This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these…
In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…
We exhibit a probabilistic algorithm which solves a polynomial system over the rationals defined by a reduced regular sequence. Its bit complexity is roughly quadratic in the B\'ezout number of the system and linear in its bit size. Our…
The box ball system is studied in the crystal theory formulation. New conserved quantities and the phase shift of the soliton scattering are obtained by considering the energy function (or $H$-function) in the combinatorial $R$-matrix.
We consider the equations which describe polytropic one-dimensional flows of viscous compressible multifluids. We prove global existence and uniqueness of a solution to the initial-boundary value problem which corresponds to the flow in a…