応用および計算数学ジャーナル

In this paper, the differential transform method (DTM) is proved to be an excellent tool to investigate analytical and numerical solutions of nonlinear ordinary differential equations. The concept of differential transformation is briefly presented and some well-known properties of this DTM are rewritten in a more generalized forms. Several classes of nonlinear differential equations are solved analytically and numerically, in order to show the efficiency of the DTM, and the fundamental algorithms are presented in Matlab language.

The importance of the electroencephalogram (EEG) rests upon the fact that it provides useful information of the normal and pathological brain functions. However, the relations among abnormal EEG, brain functions and disorders are not well known yet. We have proposed numerical quantifiers of the EEG signal, coming from the methodology of fractal mathematics and the theory of approximation. In the first part we describe an alternative to the computation of nonlinear dimensions for this kind of signals. The approach used here is based on a fractal interpolation of the data. In the second part, we describe a method for the computation of smooth complexities based on the interpolation of EEG signals by means of polynomial splines. This kind of functions is used to find quadrature formulas for the spectral moments. Both procedures are applied to treat the electroencephalographic discrimination of a group of children suffering from an Attention Deficit with Hyperactivity Disorder (ADHD).

This paper proposes a geometrical technique to obtain the value of π from splitting a circle in Equilateral triangles, a Square and Sectors. It is first ever study to calculate the value of π by splitting a circle in these shapes and then by combining areas of these shapes value of π can be calculated.