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Implementation Difficulties Analysis of Stochastic Numerical Runge-Kutta Methods
2nd International Scientific Conference "Convergent Cognitive Information Technologies", Convergent 2017, Volume 2064 von CEUR Workshop Proceedings, Seite 28--40. Moscow, CEUR-WS, (November 2017)
Zusammenfassung
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 th at 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 t he 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 moti vate 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 repos itory with the source code of discussed programs.
