The calculation of vortex method has been accelerated by using special-purpose computers, MDGRAPE-2 and MDGRAPE-3, respectively. The similar algorithm has been implemented and the improvement in speed of MDGRAPE-2 was 100 times while MDGRAPE-3 was 1000 times faster when compared with the ordinary PC Xeon 5160(3.0GHz) for N=10. In addition, the speed of MDGRAPE-3 was 25 times faster compared wit...

The asymptotic behavior of the round-off error, which accumulates when the well-known iterative method of (point) successive over-relaxation is used to solve a large-scale system of linear equations, is examined by means of a statistical model. The local round-off errors are treated as independent random variables and expressions for the mean and variance of the accumulated round-off error are ...

In the modeling of a large class of problems in science and engineering, the minimization of a functional is appeared. Finding the solution of these problems needs to solve the corresponding ordinary differential equations which are generally nonlinear. In recent years, differential transform method has been attracted a lot of attention of the researchers for solving nonlinear problems. This me...

In this study, the weather forecasting model of the National Centre for Medium Range Weather Forecasting (NCMRWF) is used for examining the characteristics of round-off-errors on three different computer architectures e PARAM 10K, SUNFIRE 6800 and Dec Alpha for several meteorological parameters such as precipitation, temperature at the surface and mid-atmosphere, and upper and lower level winds...

A verified integration algorithm is proposed for calculating s-dimensional integrals over a finite domain using numerical computations. To construct an efficient verified numerical integrator, the truncation error and the rounding error need to be considered. It has been known that interval arithmetic is one of the most efficient methods of evaluating the rounding error. However, it is much slo...

Study the interplay between roundoff error and truncation error in using the forward difference formula for the first derivative. Directory • Table of

Numerical simulations are carefully-written programs, and their correctness is based on mathematical results. Nevertheless, those programs rely floating-point arithmetic the corresponding round-off errors often ignored. This article deals with a specific simple scheme applied to advection, that particular equation from hydrodynamics dedicated transport of substance. It shows tight bound error 1...