Solving partial differential equations using multi-agent modelling

Abstract

This article studies the numerical solution of partial differential equations by Multi Agent Simulation (MAS). MAS is often used to simulate social phenomena such as traffic flow and evacuation behavior. MAS consists of agents acting autonomously and a space in which agents act. Each agent perceives its surrounding environment and interacts with each other. By the interaction, a macro phenomena emerge in the whole space from a micro one of independent agent of each agent. In order to extend the application fields of MAS technology, several works have been conducted. Among them, our research group has focussed on solving methods of linear simultaneous equations by using particle swarm optimization which is a method applying the concept of MAS. As described above, MAS is currently used in various fields and is expected to be an active field of research in the future. This study developed the method to solve partial differential equation numerically by MAS. In addition, a modeling of Stefan problem which is difficult to analyze by differential method is proposed in this study. Stefan problem is used not only in the freezing of ice, but also in various fields such as metal casting and plate tectonics theory of the earth science field, and it can be applied to various application fields when it is easily solved by MAS. This paper aims to investigate new application fields of the usage of MAS, we focus on the physical phenomena which constitute partial differential equation and propose the solution of that using the concept of MAS. Our method does not require the mathematical modelling but we solve using physical model directly.