On solving some stochastic delay differential equations by Daubechies wavelet

Abstract

There are numerous phenomena in real world that their practical modeling in mathematics language deals with differential equations. Stochastic terms have significant roles in estimating behavior of these events such as machine tool vibrations, biology, traffic dynamics, neural networks and so on, it cannot be reasonable to consider an event without its past information, and it ends up with equations including time delays. The numerical solution of stochastic delay differential equations has always been of interest to researchers. In this paper, by using scaling function of the Daubechies wavelet, a collocation method is presented to solve a class of stochastic delay differential equations and it is tried to demonstrate the advantages of using this type of wavelet. Convergence of the method is provided and numerical experiments are reported to show application of the method in practice.

Keywords:

• Stochastic delay differential equations
• scaling function
• Daubechies wavelet
• collocation method
• convergence

Acknowledgments

We are very thankful to Dr. Haman Deilami Azodi for his valuable assistance and useful comments in parts of the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).