Papers by Keyword: Numerical Example

Abstract: Black-Scholes equation is the basic equation of option pricing in financial mathematics, it is important to study its numerical solution in financial market. This paper constructs a new kind of high order accuracy numerical algorithm (Three-layer difference scheme) for Black-Scholes equation with payment of dividend. Secondly, it gives the convergence of scheme. Thirdly, the stability and error estimates are analyzed. Finally, the numerical examples show the feasibility and effectiveness of the scheme. The truncation error of Three-layer scheme is little worse than Crank-Nicolson scheme and computational cost is little better than Crank-Nicoslon scheme. Therefore, the scheme is better suitable for applying to calculate the option pricing in the demanding high level of instantaneity.

Abstract: In injection mold, design of gate location is among the most critical factors in achieving dimensionally accurate parts and high productivity of the molding process, since it influences the manner in which the plastic flows into the mold cavity. To automatically predict the optimal gate location of injection molds based on injection-molding simulation, a new and practical method: empirical search method according to the analysis of common optimization methods has been presented in this article. In this method, the gate location scope is initiated by the practical experience of mold designer so that the core for the gate location optimization is construction of empirical library. In order to build the empirical library, in terms of shape and function characteristic of injection-molding part, all the parts are classified six kinds: shell, container, plate, structural part, ornamental part and transparent part, and the corresponding design rules are kept in the empirical library. In addition, this article combines the empirical search method and numerical simulation technique, builds the mathematics model for the gate location optimization of plate part in empirical library and obtains the gate location optimization scheme for this kind of part through one concrete numerical example. The analysis and verification by adopting the software Moldflow testify the optimization mathematics model is effective.