N-body simulations of the Sun, the planets,
and small celestial bodies are frequently used to model the evolution of the Solar
System. Large numbers of numerical integrators for performing such simulations
have been developed and used; see, for example, [1,2]. The primary
objective of this paper is to analyse and compare the efficiency and the error
growth for different numerical integrators. Throughout the paper, the
error growth is examined in terms of the global errors in the positions and
velocities, and the relative errors in the energy and angular momentum of the
system. We performed numerical experiments for the different integrators
applied to the Jovian problem over a long interval of duration, as long as one
million years, with the local error tolerance ranging from 10-16 to 10-18.
Simulation has become the
evaluation method of choice for many areas of distributing computing research.
Simulation has been applied successfully for modeling small and large complex
systems and understanding their behavior, especially in the area of distributed
systems or parallel environment. The aim of my research is to study and
qualitative analysis of simulation on a single server & on distributed
environment and finding the related issues & its comparison.
balance modeling is regarded as a universally accepted mathematical framework
for dynamic simulation of various particulate processes, such as
crystallization, granulation and polymerization. This article is concerned with
the application of the method of characteristics (MOC) for solving population
balance models describing batch crystallization process. The growth and
nucleation are considered as dominant phenomena, while the breakage and aggregation
are neglected. The numerical solutions of such PBEs require high order accuracy
due to the occurrence of steep moving fronts and narrow peaks in the solutions.
The MOC has been found to be a very effective technique for resolving sharp
discontinuities. Different case studies are carried out to analyze the accuracy
of proposed algorithm. For validation, the results of MOC are compared with the
available analytical solutions and the results of finite volume schemes. The
results of MOC were found to be in good agreement with analytical solutions and
superior than those obtained by finite volume schemes.