Implementation difficulties analysis of stochastic numerical rungekutta methods

This article discusses stochastic numerical methods of Runge-Kutta methods with weak and strong convergences for systems of stochastic differential equations in the Ito form. At first section we give a brief review of main works on the topic. In next section we make short introduction into theory of stochastic numerical methods and facts from the theory of stochastic differential equations. Due to the fact that the analytical solution exists only for a small subset of stochastic differential equations, stochastic numerical methods are the only way to obtain the solution. Stochastic Runge-Kutta methods are based on the same ideas as the classic methods, but their scheme is essentially more complicated than their deterministic counterparts. This leads to difficulties when one attempts to implement them. In this paper we motivate the approach to the implementation of these methods using source code generation as it allows achieving universality while maintaining a simplicity of code. We discuss some of the implementation details and the used programming languages and libraries. We give several examples of stochastic differential equations, used to test the program and evaluate the error of the calculations. We provide the link to the repository with the source code of discussed programs. © 2017 CEUR-WS. All rights reserved.