Related papers: A scheme for solving hyperbolic problems with symb…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our…
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…
Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem,…
In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
We consider the ultrahyperbolic equation in the Euclidean space. The behavior at the infinity of a certain class of solutions is studied. We examine the issue of existence of solutions to the scattering problem: for a given asymptotics at…
Consider the Poincare disc model for hyperbolic geometry. In this paper, a convenient computational formula is developed along with an aesthetic geometric interpretation. Two proofs, one geometric and one analytical, of each result are…
With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are…
This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". The first part is entitled "Existential questions in…
We are motivated to approximate solutions of a Hodgkin-Huxley type model with implicit methods. As a representative we chose a psychiatric disease model containing stable as well as chaotic cycling behaviour. We analyze the bifurcation…
We explore the three-body problem in two dimensions using the adiabatic hyperspherical representation. We develop the main equations in terms of democratic hyperangular coordinates and determine several symmetry properties and boundary…
This work is concerned with relaxation models arising from numerical schemes for hyperbolic-parabolic systems. Such models are a hyperbolic system with both the hyperbolic part and the stiff source term involving a small positive parameter,…