Related papers: Singularly perturbed discrete differential equatio…
A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be…
In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to compare and contrast the different results by proposing a…
A singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise-uniform Shishkin mesh. Scaled discrete derivatives (with scaling…
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…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…
Consider a singularly perturbed ordinary differential equation, admitting 0 as turning point of order p. We study the behaviour, in the complex plane, of the solutions of this equation in the neighborhood of 0. We prove that the domain of…
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…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular…
This paper studies the problem of perturbed convex and smooth optimization. The main results describe how the solution and the value of the problem change if the objective function is perturbed. Examples include linear, quadratic, and…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
We consider a perturbed ordinary differential equation where the perturbation is only significant when a one-dimensional null recurrent diffusion is close to zero. We investigate the first order correction to the unperturbed system and…
We consider asymptotically stable scalar difference equations with unit-norm initial conditions. First, it is shown that the solution may happen to deviate far away from the equilibrium point at finite time instants prior to converging to…