In this paper, spline approximations with five collocation points are used for the
numerical simulation of stochastic of differential equations(SDE). First, we have modeled
continuous-valued discrete wiener process, and then numerical asymptotic st
ochastic
stability of spline method is studied when applied to SDEs. The study shows that the
method when applied to linear and nonlinear SDEs are stable and convergent.
Moreover, the scheme is tested on two linear and nonlinear problems to illustrate
the applicability and efficiency of the purposed method. Comparisons of our results with
Euler–Maruyama method, Milstein’s method and Runge-Kutta method, it reveals that the
our scheme is better than others.