A nodal spline interpolant for the Gregory rule of even order.
A nonasymptotic theorem for unnormalized Feynman–Kac particle models
We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first...
A Nonconforming Combined Method for Solving Laplace's Boundary Value Problems with Singularities.
A Nonconforming Finite Element Method to Compute the Spectrum of an Operator Relative to the Stability of a Plasma in Toroidal Geometry.
A non-convex diffusion model for simultaneous image denoising and edge enhancement.
A nonhomogeneous backward heat problem: regularization and error estimates.
A nonlinear adaptative multiresolution method in finite differences with incremental unknowns
A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines
A nonlinear system of differential equations with distributed delays
It is well-known that the environments of most natural populations change with time and that such changes induce variation in the growth characteristics of population which is often modelled by delay differential equations, usually with time-varying delay. The purpose of this article is to derive a numerical solution of the delay differential system with continuously distributed delays based on a composition of -step methods () and quadrature formulas. Some numerical results are presented compared...
A nonmonotone line search for the LBFGS method in parabolic optimal control problems
In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Finally the...
A nonnegatively constrained trust region algorithm for the restoration of images with an unknown blur.
A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem
This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way,...
A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem***
This study is mainly dedicated to the development and analysis of non-overlapping domain decomposition methods for solving continuous-pressure finite element formulations of the Stokes problem. These methods have the following special features. By keeping the equations and unknowns unchanged at the cross points, that is, points shared by more than two subdomains, one can interpret them as iterative solvers of the actual discrete problem directly issued from the finite element scheme. In this way,...
A nonsmooth optimisation approach for the stabilisation of time-delay systems
This paper is concerned with the stabilisation of linear time-delay systems by tuning a finite number of parameters. Such problems typically arise in the design of fixed-order controllers. As time-delay systems exhibit an infinite amount of characteristic roots, a full assignment of the spectrum is impossible. However, if the system is stabilisable for the given parameter set, stability can in principle always be achieved through minimising the real part of the rightmost characteristic root, or...
A nonsmooth optimisation approach for the stabilisation of time-delay systems
This paper is concerned with the stabilisation of linear time-delay systems by tuning a finite number of parameters. Such problems typically arise in the design of fixed-order controllers. As time-delay systems exhibit an infinite amount of characteristic roots, a full assignment of the spectrum is impossible. However, if the system is stabilisable for the given parameter set, stability can in principle always be achieved through minimising the real part of the rightmost characteristic...
A nonsmooth version of the univariate optimization algorithm for locating the nearest extremum (locating extremum in nonsmooth univariate optimization)
An algorithm for univariate optimization using a linear lower bounding function is extended to a nonsmooth case by using the generalized gradient instead of the derivative. A convergence theorem is proved under the condition of semismoothness. This approach gives a globally superlinear convergence of algorithm, which is a generalized Newton-type method.
A nonstandard dynamically consistent numerical scheme applied to obesity dynamics.
A note concerning Gauss-Jackson method.
Specialized literature concerning studies on Orbital Dynamics usually mentions the Gauss-Jackson or sum squared (∑2) method for the numerical integration of second order differential equations. However, as far as we know, no detailed description of this code is available and there is some confusion about the order of the method and its relation with the Störmer method. In this paper we present a simple way of deriving this algorithm and its corresponding analog for first order equations from the...
A note on -point conservative monotone schemes
First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a -point monotone scheme may give an oscillatory solution even though...
A note on (2K+1)-point conservative monotone schemes
First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a (2K+1)-point monotone scheme may give an oscillatory solution even...