We propose a new numerical method for the computation of the optimal value function of perturbed control systems and associated globally stabilizing optimal feedback controllers. The method is based on a set oriented discretization of state space in combination with a new algorithm for the computation of shortest paths in weighted directed hypergraphs. Using the concept of a multivalued game, w...

Original scientific paper This paper presents semi-analytical solution for the problem of elastic impact of two beams. The solution is based on the finite element discretization of the structure and equation of motion solution using diagonalization method for solving a system of differential equations. This procedure avoids temporal discretization typical for numerical methods, and in this way ...

This work is devoted to the numerical study of the Cahn-Hilliard equation with dynamic boundary conditions. A spatial finite-volume discretization is proposed which couples a 2d-method in a smooth connected domain and a 1d-method on its boundary. The convergence of the sequence of approximate solutions is proved and various numerical simulations are given.

The transport and continuum equations exhibit a number of conservation laws. For example, scalar multiplication is conserved by the transport equation, while positivity of probabilities is conserved by the continuum equation. Certain discretization techniques, such as particle based methods, conserve these properties, but converge slower than spectral discretization methods on smooth data. Stan...

The quasi-geostrophic equations (QGE) are usually discretized in space by the finite difference method. The finite element (FE) method, however, offers several advantages over the finite difference method, such as the easy treatment of complex boundaries and a natural treatment of boundary conditions [61]. Despite these advantages, there are relatively few papers that consider the FE method app...

A numerical method for a singular perturbation problem with a turning point is considered. The method uses non-equidistant discretization meshes. The first order accuracy, uniform in the perturbation parameter is proved in the discrete L1 norm.

This paper investigates an initial-boundary value problem with nonlocal condition for the wave equation. The numerical solution is developed by using Homotopy perturbation method. This method is based on the use of traditional perturbation method and homotopy technique. Using this method, a rapid convergent series solution can be obtained in most cases. Furthermore, this method does not require...

The multiple exchange algorithm for restricted range approximation is discussed. Efficient formulas are derived for the numerical implementation of the method. Discretization effects are analyzed mathematically. The method is applied to a certain problem arising in digital filter design.

The aim of this paper is to give a detailed effect of several parameters such as step height, Reynolds number, contraction ratio, and temperature difference between the entrance and solid boundaries, of a forward-facing step. An accurate length of separation and reattachment zones are achieved. A finite-volume method (FVM) has been developed to study incompressible flow in a forward-facing step...

The effect of ergodisation (either by additional coils like in TEXTOR-DED or by intrinsic plasma effects like in W7-X) defines the need for transport models being able to describe this properly. A prerequisite for this is the concept of local magnetic coordinates allowing a correct discretization with minimized numerical errors [1]. For these coordinates the full respective metric tensor has to...