A comparison of the iterative method and Picard's successive approximations for deterministic and stochastic differential equations

摘要

A comparison of Adomian's iterative method for stochastic differential equations and the Picard method of successive approximations shows interesting differences for both deterministic and stochastic differential equations. The iterative procedure is more efficient and computationally useful even in the deterministic case. In the stochastic case, the Picard method has no value, while the iterative procedure is useful and simple.