A mixed-method to numerical simulation of variable order stochastic advection diffusion equations

Abstract

The study of stochastic problems is very important and there is an increasing demand for investigating the behavior of a number of sophisticated dynamical systems in different areas of science as well as in engineering and finance. In this paper, we present a method which is based on the collocation method (CM) and the operational matrix method (OMM) by using Hosoya polynomials (HPs). This mixed-method helps us to convert the stochastic problems into a system of algebraic equations to access a solution of such problems. One of the most important advantages of this method is the simulation of the noise terms at the collocation points. Finally, two types of the VO–SADEs are simulated and tested via the proposed technique to confirm the superiority and accuracy.

Keywords

• Stochastic advection diffusion equations
• Hosoya polynomials
• Operational matrix
• Collocation points