The article deals with the minimum-time running problem. The time of covering a given distance is minimized. The Hill-Keller model of running employed is based on Newton's second law and the equation of power balance. The problem is formulated in optimal control. The unknown function is the runner's velocity that varies with the distance. The problem is solved applying the direct Chebyshev's ps...

Numerical simulation is now an acceptable mode of inquiry into a wide range of physical phenomena. As computational methods and hardware continue to advance, it is often the case that older, legacy applications no longer implement the best technology for solving a problem and must be updated. Once modified, these applications need to be extensively studied to ensure that they retain the importa...

As discussed in the companion paper [J. B. Witkoskie and J. S. Cao, J. Chem. Phys. 121, 6361 (2004), preceding paper], quantitative extraction of information from single molecule experiments by several proposed indicators is difficult since the experiments only observe certain characteristics of the system, even though the indicators can contain all available information. This paper shows how o...

Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia questions notions generally held as “laws of nature” by practitioners of numerical computing: 1. High-level dynamic programs have to be slow, 2. One must protot...

Variational data assimilation problems are concerned with computing unknown initial values for the simulation and prediction of natural phenomena, most notably in weather prediction, and are usually solved via an ill-posed optimal control problem for the initial state at the time of the first available measurements. An alternative “forward” approach focuses on computation of the final state aft...

Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein’s equations with the harmonic slicing condition is presented. Significant errors in the mass function are shown to arise from the steep gradient zone behind the black hole horizon, which challenge the Computational Fluid Dyna...

in this paper, a new and ecient approach is applied for numerical approximationof the linear dierential equations with variable coecients based on operational matriceswith respect to hermite polynomials. explicit formulae which express the hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of theoriginal expansion coecients of the function itse...

in this paper, we present a capable algorithm for solving a class of nonlinear optimal control problems (ocp's). the approach rest mainly on the differential transform method (dtm) which is one of the approximate methods. the dtm is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. utilizing this approach, the optim...

in this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.in the first approach, the equilibrium point of the system is one of the centers of the related membership fu...