Issues in the software implementation of stochastic numerical Runge–Kutta

Abstract

This paper discusses the application of stochastic Runge-Kutta-like numerical methods with weak and strong convergences for systems of stochastic differential equations in Itô form. At the beginning a brief overview of available publications about stochastic numerical methods and information from the theory of stochastic differential equations are given. Then the difficulties that arise when trying to implement stochastic numerical methods and motivate to use source code generation are described. We discuss some implementation details, such as program languages (Python, Julia) and libraries (Jinja2, Numpy). Also the link to the repository with source code is provided in the article.