Abstract: As is known, one of the priority directions of research
works of natural sciences is introduction of applied section of
contemporary mathematics as approximate and numerical methods to
solving integral equation into practice. We fare with the solving of
integral equation while studying many phenomena of nature to whose
numerically solving by the methods of quadrature are mainly applied.
Taking into account some deficiency of methods of quadrature for
finding the solution of integral equation some sciences suggested of
the multistep methods with constant coefficients. Unlike these papers,
here we consider application of hybrid methods to the numerical
solution of Volterra integral equation. The efficiency of the suggested
method is proved and a concrete method with accuracy order p = 4
is constructed. This method in more precise than the corresponding
known methods.
Abstract: Nowadays, the plant location selection has a critical
impact on the performance of numerous companies. In this paper, a
methodology is presented to solve this problem. The three decision
making methods, namely Delphi, AHP and improved VIKOR, are
hybridized in order to make the best use of information available
based on the decision makers or experts. In this respect, the aim of
using Delphi is to select the most influential criteria by a few decision
makers. The AHP is utilized to give weights of the selected criteria.
Finally, the improved VIKOR method is applied to rank alternatives.
At the end of paper, an application example demonstrates the
applicability of the proposed methodology.
Abstract: In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.