An important question for human balance control concerns how the differential equations for the neural control of balance should be formulated. In this paper, we consider a discrete-time and a continuous-time delayed proportional-derivative-acceleration controller and establish the transition between them by means of the semi-discretization. We show that the critical delay, which limits stabili...

We prove enhanced error estimates for high order semi-lagrangian discretizations of the Vlasov-Poisson equation. It provides new insights into optimal numerical strategies for the numerical solution of this problem. The new error estimate O ( min ( ∆x ∆t , 1 ) ∆x + ∆t ) is based on advanced error estimates for semi-lagrangian schemes, also equal to shifted Strang’s schemes, for the discretizati...

Here is a (possibly infinite) index set, R 1⁄4 R [ fþ1g [ f 1g denotes the extended real line, f : R ! R and g : R !R. The above optimization problem is performed in the finite-dimensional space R and, if the index set is infinite, is a subject to an infinite number of constraints, therefore it is referred to as a SIP problem. There are numerous applications which lead to SIP problems. We can r...

A system of semi-discrete coupled nonlinear Schrödinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schrödinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further...

In this paper we construct and study discretizations of a nonlinear Zakharov-wave system occurring in plasma physics. These systems are generalizations of the Zakharov system that can be recovered by taking a singular limit. We introduce two numerical schemes that take into account this singular limit process. One of the scheme is conservative but sensible to the polarization of the initial dat...

Unwanted relative vibrations between the tool and the workpiece represent significant challenges in high-speed machining. In order to avoid this problem, one needs to specify ranges for system parameters (spindle speed, depth of cut) for which the process is stable, i.e., to obtain a so-called stability chart. Such stability charts usually can only be given by numerical means which is illustrat...

The bidomain model is a system of partial differential equations used to model the propagation of electrical potential waves in the myocardium. It is composed of coupled parabolic and elliptic partial differential equations, as well as at least one ordinary differential equation to model the ion activity through the cardiac cell membranes. The purpose of this paper is to propose and analyze sev...

We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an anti-symmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to already known systems. ...

Discretization is a fundamental step in numerical analysis for the problems described by differential equations, and difference between continuous model discrete one of most important problems. In this paper, we consider effect time-dependent propagation speed on energy estimate solutions wave equation semi-discrete which discretization with respect to space variables.

We consider the generalization of a variant of Karmarkar's algorithm to semi-infinite programming. The extension of interior point methods to infinite-dimensional linear programming is discussed and an algorithm is derived. An implementation of the algorithm for a class of semi-infinite linear programs is described and the results of a number of test problems are given. We pay particular attent...