Application of Multiple Scale Method to a Discretized Financial PDE

This paper presents an application of two way variable expansion method (multiple scale) for the calculation of the periodic solutions, resulted from a Hopf bifurcation of a discretized generic PDE in finance to a first order time-delay system arising from laser dynamics and a single inertial neural model with time delay. The two way variable expansion methods involve easy computation only, and yield estimation to the oscillatory movement of the price of stock with high accuracy.