Numerical solution of Heun equation via linear stochastic differential equation

In this paper, the numerical approach of the following Stochastic differential equation which is named ”Heun equation”, will be represented. such that ; ; ; ; and , could be coefficients of Gaussian random numbers which isnamed wiener process. Making linear equations system from this equation, it could besolved by computing fundamental matrix of this system, with different methods. Finally,this stochastic equation is solved by numerical methods like E.M. and Milstein. Also itsasymptotic stability and statistical concepts like expectation and variance of solutions arediscussed.

Keywords:

Heun Equation , Stochastic Differential Equation , Linear Equations System , Gaussian Random Numbers