Related papers: Recursive divergence formulas for perturbing unsta…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
A parametric numerical study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out. The computations are performed by a numerical approach verified against independent…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…
The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general $p$th-order bifurcating autoregressive processes, under…
We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a…
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…
We derive and prove the path-kernel formula for the linear response (parameter-derivative of averaged statistics) of SDEs. The parameter may affect the drift coefficient, the diffusion coefficient, and the initial condition. The formula…
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high…
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…
Differential sensitivity measures provide valuable tools for interpreting complex computational models used in applications ranging from simulation to algorithmic prediction. Taking the derivative of the model output in direction of a model…
This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an…
An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and the parametric derivatives of statistical quantities are…
We consider a linear differential system of Mathieu equations with periodic coefficients over periodic closed orbits and we prove that, arbitrarily close to this system, there is a linear differential system of Hamiltonian damped Mathieu…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
We examine a strange chaotic attractor and its unstable periodic orbits in case of one degree of freedom nonlinear oscillator with non symmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a…
Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic…
We present a computational analysis of a 2$\times$2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in…
We study linear response for families of skew-product dynamical systems with contracting fibres. Our approach is based on a sectional transfer operator acting on families of probability measures along the fibres. The operator allows to…