Abstract
We have developed and designed a problem solving enviroment(PSE), called DISTRAN which generates a fortran simulation program based on partial differential equations(PDEs). One of key issues in PSE and also scientific simulation is to determine a stable time-step size Δ t and to reduce computation CPU time. Usually Δ t is common for one set of grids. In this paper we propose an Individual Time Step(ITS) for Runge-Kutta Method, in which each grid has an individual Δ t which is variable depending on each grid point. In DISTRAN, each individual-time-step Δ t is automatically determined to be stable in Runge-Kutta Fehlberg Method. Even if PDEs have stiff problems, we can solve the difficulty of stability and reduce the CPU time in DISTRAN. DISTRAN implements the ITS method automatically and provides a fortran program to users.
