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

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.