Parallel Numerical Creation of Phase-space Diagrams of Nonlinear Systems Using Maple

Abstract

In this paper the numerical creation of phase-plane diagrams in parallel utilizing Maple is presented. One of the most effective method for studying nonlinear systems is the creation of detailed enough phase-plane diagrams. But in the case of large systems it requires huge amount of numerical calculation, which can be accelerated using parallel computers. Here we show some attempts for this using moderate size known problems. We demonstrate that detailed diagrams can be created fast and efficiently with a SIMD model based algorithm even using simple PC-s. We exhibit that the parallel algorithm taken for one- and two-dimensional problems can be expanded for 3D phase-space diagram creation without any loss of efficiency. In this paper a methodology is showed which can be followed in the study of large dynamical systems as well.

Sensitivity Study of a Nonlinear Semi-Active Suspension System

“…Later the global sensitivity analysis of the system will be also carried out to acquire more comprehensive knowledge about the behaviour of systems. Another important task is to speed up with parallelization [22]- [24] and to further develop the method in a way to be effectively used in control theory tasks. A long term task is to utilize an optimization algorithm to adjust the parameters to gain an optimal solution in order to reduce the sensitivity of the system.…”