In this paper we describe the classical methods used to solve the Euler equations. Special attention is devoted to the iterative method based on a contraction mapping derived from these equations in Maldonado and Moreira (2003). We test the numerical robustness of this method when it is used in models with sensitiveness to initial conditions. Finally we extend the method to the case of stochast...

It has been an open problem to derive a necessary and sufficient condition for a linear tensor product problem to be weakly tractable in the worst case. The complexity of linear tensor product problems in the worst case depends on the eigenvalues {λi}i∈N of a certain operator. It is known that if λ1 = 1 and λ2 ∈ (0, 1) then λn = o((lnn)−2), as n → ∞, is a necessary condition for a problem to be...

Background: Muscle fatigue has been known to influence brain activity, but very little is known about how cortical centers respond to muscle fatigue.Objective: This study was conducted to investigate the effects of muscle contraction and fatigue induced by two different percents of maximal voluntary contraction (MVC) on Electroencephalography (EEG) signals.Material and Methods: In t...

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: { D t x(t) = f(t, x(t), D β t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = ∫ 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle. Keywords—Fractional differential equation; Integral boundary condi...