1. Dijkstra Algorithm in Transportation Systems at Kediri’s Central Post Office

Aprilia Dwi Handayani

Universitas Nusantara PGRI Kediri, East Java, Indonesia.

Abstract:

One of the graph role in everyday life is to determine the shortest path, including public transportation, service delivery, and to search nearby locations (eg hotels, hospitals, railway stations, tourist sites, etc.). By knowing the nearest location, the place will be reached with faster time, in addition, we can also save costs. In the field of correspondence through the post office, the determination of the alternative pathway for effective and efficient in the delivery of mail and goods by postmen need role graph theory. Alternative path is the path taken by the postman choice when making the delivery process thus accelerate the journey to the destination. One way that can be applied to determine the shortest path in the delivery of mail is to use Dijkstra’s algorithm. This algorithm aims to find the shortest path based on the weight of the smallest from one point to another. Suppose point line depicts a portrait of buildings and roads, Dijkstra’s algorithm calculates all possible weight to the smallest of any point. The purpose of this study are to: 1) Describe the problems of the mail and goods transport distributions system in Kediri’s Post Office in the form of graphs, and 2) Describe the shortest route in the mail and goods transport distributions system in Kediri’s Post Office by using dijkstra’s algorithm.

The results of this study that are explained in this paper is the problem of the transport systems in Kediri’s Central Post Office and describie the solution for it. It means that this paper will explain the alternatives pathway for the effective and efficient in the delivery of mail and good in Kediri’s Central Post Office. In addition, also as a consideration for the relevant authorities, in this case the Kediri’s Post Office to take the shortest route policy in the distribution of mail and goods.

Keywords: Dijkstra Algorithm.

2. Comparison of Numerical Methods for Solving Stochastic Differential Equations with Time Delay

Hamit Mirtagioglu, Akbar Barati Chiyaneh

Department of Mathematics, University of Bitlis Eren, Bitlis, Turkey.

Abstract: In this paper, we have presented computational methods for solving stochastic differential equations (SDDEs) with distuributed delay term in the drift and diffusion cofficient. Our purpose is comparatively investigates some numerical methods to solve stochastic delay differential equations. We indicate the nature of the methods of interest and examine convergence of them. By presenting some numerical experiments we illustrate the theorical results and finally the results numerical methods are supported with graphs and error tables and discussed about which method is useful and superior and in which cases these methods can be used.

Keywords: Stochastic delay differential equations, Strong Solutions, Numerical Methods, Strong and weak convergence.