In this paper, the numerical stability and accuracy of Precise Time Step Integration Method are discussed in detail. It is shown that the method is conditionally stable and it has inherent algorithmic damping, algorithmic period error and algorithmic amplitude decay. However for discretized structural models, it is relatively easy for this time integration scheme to satisfy the stability conditions and required accuracy. Based on the above results, the optimum values of the truncation order L and bisection order N Unbelievable Men Nike LunarGlide+4 Deep Blue
are presented. The Gauss quadrature method is used to improve the accuracy of the Precise Time Step Integration Method. Finally, two numerical examples are presented to show the feasibility of this improvement method.
The multi-dimensional Black–Scholes equation is solved numerically for a European call basket option using a priori–a posteriori error estimates. The equation is discretized by a finite difference method on a Cartesian grid. The grid is adjusted dynamically in space and time to satisfy a bound on the global error. The discretization errors in each time step are estimated and weighted by the solution of the adjoint problem. Bounds on the local errors and the adjoint solution are obtained by the maximum principle for parabolic equations. Comparisons are made with Monte Carlo and quasi-Monte Carlo methods Roshe0313-Shoes Roshe Trainers Men Black Gray Blue
in one dimension, and the performance of the method is illustrated by examples in one, two, and three dimensions.