[1] A superposed epoch analysis of 100–300 substorms is performed to determine the median size and shape of the substorm-associated VLF chorus, magnetic bay, and Pi2 pulsation burst observed at the near-auroral Halley research station, Antarctica, and at the midlatitude Faraday station at three different local times (2230, 2330, 0130 MLT). The spatial and temporal properties of the magnetic bay...

We study the dynamics of a family of third-order iterative methods that are used to find roots of nonlinear equations applied to complex polynomials of degrees three and four. This family includes, as particular cases, the Chebyshev, the Halley and the super-Halley root-finding algorithms, as well as the so-called c-methods. The conjugacy classes of these iterative methods are found explicitly....

Experimentation and the evaluation of algorithms have a long history in algebra. In this paper we follow single test example over more than 250 years. 1685, John Wallis published A treatise algebra, both historical practical, containing solution Colonel Titus’ problem that was proposed to him around 1650. The Titus consists three algebraic quadratic equations unknowns, which transformed into fi...

In this paper, we present a new third-order family of iterative methods in order to compute the multiple roots nonlinear equations when multiplicity (m?1) is known advance. There plethora point-to-point methods, available literature; but our are based on geometric derivation and converge required zero even though derivative becomes or close vicinity zero. We use exponential fitted curve tangenc...

The Powell singular function was introduced 1962 by M.J.D. Powell as an unconstrained optimization problem. The function is also used as nonlinear least squares problem and system of nonlinear equations. The function is a classic test function included in collections of test problems in optimization as well as an example problem in text books. In the global optimization literature the function ...

We present another simple way of deriving several iterative methods for solving nonlinear equations numerically. The presented approach of deriving these methods is based on exponentially fitted osculating straight line. These methods are the modifications of Newton’s method. Also, we obtain well-known methods as special cases, for example, Halley’s method, super-Halley method, Ostrowski’s squa...

Previous research has shown that the study of global electrical circuit can be relevant to climate change studies, and this done through measurements potential gradient near surface in fair weather conditions. However, highly variable due different local effects (e.g., pollution, convective processes). In order try minimize these effects, performed at remote locations where anthropogenic influe...