Equivalent One-dimensional Equation Research Articles

Certain Algebraic Test for Analyzing Aperiodic Stability of Two-Dimensional Linear Discrete Systems

This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.

Improved Additive Operator Splitting Algorithms for Basket Option Pricing Model

In order to solve Black-Scholes equation of basket option pricing model by numerical method. This paper used Additive Operator Splitting (AOS) algorithm to split the multi-dimensional Black-Scholes equation into equivalent one-dimensional equation set, and constructed 'Explicit-Implicit' and 'Implicit-Explicit' schemes to solve it. Then compatibility, stability and convergence of those schemes were analyzed. Finally, this paper compared computation time and precision of the schemes through numerical experiments. 'Explicit-Implicit' and 'Implicit-Explicit' schemes of AOS algorithms have both higher accuracy and faster computing speed and them have practical significance in solving basket option pricing model.

Driving of a single vortex in a long Josephson junction

The driving of a single vortex by a bias current in a long Josephson junction with a finite width has been studied with the two-dimensional Josephson equation. The applicable range of the equivalent one-dimensional equation is shown.