Various issues related to the development of a new code for nonstiff differential equations are discussed. This code is based on two-step Runge-Kutta methods of order five and stage order five. Numerical experiments are presented which demonstrate that the new code is competitive with the Matlab ode45 program for all tolerances.
Universal tracking control is investigated in the context of a class of -input, -output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary -valued reference signal of class (absolutely...
Universal tracking control is investigated in the context of a class S of M-input, M-output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary -valued reference signal r of class W1,∞ (absolutely...
The method of transfer of boundary conditions yields a universal frame into which most methods for solving boundary value problems for ordinary differential equations can be included. The purpose of this paper is to show a possibility to extend the idea of transfer of conditions to a particular twodimensional problem.
Numerical solution of linear boundary value problems for ordinary differential equations by the method of transfer of conditions consists in replacing the problem under consideration by a sequence of initial value problems. The method of transfer for systems of equations of the first order with Lebesque integrable coefficients was studied by one of the authors before. The purpose of this paper is to extend the idea of the transfer of conditions to singular boundary value problems for a linear second-order...
A survey of investigations of linear differential equations from the point of view of transformations is described. These investigations started in the middle of the last century and continued till the present time. Essential step was done in the fifties by O. Borvka, who started global investigations of the second order equations.