On the -stability of impulsive dynamic system on time scales.
On the -dichotomy for homogeneous linear differential equations.
On third order advanced nonlinear differential equations
On those ordinary differential equations that are solved exactly by the improved Euler method
As a numerical method for solving ordinary differential equations , the improved Euler method is not assumed to give exact solutions. In this paper we classify all cases where this method gives the exact solution for all initial conditions. We reduce an infinite system of partial differential equations for to a finite system that is sufficient and necessary for the improved Euler method to give the exact solution. The improved Euler method is the simplest explicit second order Runge-Kutta method....
On time reparametrizations and isomorphisms of impulsive dynamical systems
We prove that for a given impulsive dynamical system there exists an isomorphism of the basic dynamical system such that in the new system equipped with the same impulse function each impulsive trajectory is global, i.e. the resulting dynamics is defined for all positive times. We also prove that for a given impulsive system it is possible to change the topology in the phase space so that we may consider the system as a semidynamical system (without impulses).
On time transformations for differential equations with state-dependent delay
Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.
On total truncation error estimation for the one-step method
In this paper the author establishes estimation of the total truncation error after steps in the fifth order Ruge-Kutta-Huťa formula for systems of differential equations. The approach is analogous to that used by Vejvoda for the estimation of the classical formulas of the Runge-Kutta type of the 4-th order.
On transformations of bundles of solutions of a fourth order iterated linear differential equation
On transformations of differential equations and systems with deviating argument
On transformations of functional-differential equations
The paper contains applications of Schrőder’s equation to differential equations with a deviating argument. There are derived conditions under which a considered equation with a deviating argument intersecting the identity can be transformed into an equation with a deviation of the form . Moreover, if the investigated equation is linear and homogeneous, we introduce a special form for such an equation. This special form may serve as a canonical form suitable for the investigation of oscillatory...
On Transformations of Graded Matrices, with Applications to Stiff ODE's.
On transformations of self-adjoint linear differential systems and their reciprocals
On transformations of self-adjoint linear differential systems
On transformations of singular quadratic functionals corresponding to equation
On transformations of two homogeneous linear second order differential equations of a general and of Sturm forms
On transformations of two linear second order differential equations
On transformations of functional-differential equations
On transformations of ordinary differential equations
The paper describes the general form of an ordinary differential equation of the order which allows a nontrivial global transformation consisting of the...
On two transfer principles in stochastic differential geometry
On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves.