Abstract
Two modified versions of the stochastic Heun method which is an explicit method for stochastic differential equations(SDEs) are presented in this paper. We call them the modified Heun method. It is shown that the modified Heun method has order of strong convergence 1 for scalar SDEs with scalar noise. Its stability analysis is also studied and it is concluded that the modified Heun method is superior to the stochastic Heun method with respect to mean-square and asymptotic stability.
