The aim of this book is to use a semi-analytic technique for solving singular initial value problems of ordinary differential equations with a singularity of different kinds to construct polynomial solution using two point osculatory interpolation. The efficiency and accuracy of suggested method is assessed by comparisons with exact and other approximate solutions for a wide classes of non-homogeneous, non-linear singular initial value problems. Many examples are presented to demonstrate the applicability and efficiency of the suggested method on one hand and to confirm the convergence order...

In this book an electric power system is considered, we design mathematical model for the determination of the increase in operational cost of transmission line caused by reactive power transmission, and decrease the Losses in electric power system by derived mathematical relations to determine an economically justified transmission distance for VARs transmission. Also, detailed analyses to help determine the increase in production costs due to the transmission of reactive power are given. The main purpose of the book is to introduce the detailed analyses of artificial neural networks...

In this book, the eigenvalue problems for ordinary differential equation with boundary conditions is considered. We proposed the semi analytic technique to solve non - singular eigenvalue problems using osculator interpolation. The technique finds the eigenvalue and the corresponding nonzero eigenvector which represent the solution of the problem in a certain domain. Many applications in mathematical physics and electromagnetic or elastic wave equations, chemical reaction theory, radiative heat transfer and nanotechnology such the Mathieu differential equation and Bratu equation are presented.