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A practical and new Runge--Kutta numerical scheme for stochastic differentialequations is explored. Numerical examples demonstrate the strong convergence ofthe method. The first order strong convergence is then proved using Itointegrals for both Ito and Stratonovich interpretations. As a straightforwardmodification of the deterministic Improved Euler/Heun method, the method is agood entry level scheme for stochastic differential equations, especially inconjunction with Higham's introduction [SIAM Review, 43:525--546, 2001].

Modify the Improved Euler scheme to integrate stochastic differential equations