Directional transition matrix
We present a generalization of topological transition matrices introduced in [6].
Dynamics of systems with Preisach memory near equilibria
We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can also appear...
Enclosures and semi-analytic discretization of boundary value problems
Étude des solutions surstables de l'équation de Van der Pol
Exponential functions as boundary layer functions.
Exponentially fitted spline approximation method for solving selfadjoint singular perturbation problems.
Finite-difference method for parameterized singularly perturbed problem.
Fonctions Généralisées et Analyse Non Standard.
Higher order singular perturbation method for linear differential equations in Banach spaces
High-order methods for semilinear singularly perturbed boundary value problems.
Improvement of Numerical Solution of Boundary Layer Problems by Incorporation of Asymptotic Approximations.
Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations
Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.
L1 and L... Uniform Convergence of a Difference Scheme for a Semilinear Singular Perturbation Problem.
Lower semicontinuous differential inclusions. One-sided Lipschitz approach
Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in [4]. Using the main idea of [10], we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.
Mean time for the development of large workloads and large queue lengths in the GI/G/1 queue.
Minimum principle for quadratic spline collocation discretization of a convection-diffusion problem
Mixed type semicontinuous differential inclusions in Banach spaces
We consider a class of differential inclusions in (nonseparable) Banach spaces satisfying mixed type semicontinuity hypotheses and prove the existence of solutions for a problem with state constraints. The cases of dissipative type conditions and with time lag are also studied. These results are then applied to control systems.
-widths for singularly perturbed problems
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
Nonlinear singularly perturbed systems of differential equations: A survey.