Stochastic solutions with derivatives and non-polynomial terms: The scrape-off layer equations

The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are used. This paper deals with the problems that arise when the nonlinear terms are nonpolynomial or involve derivatives. A set of equations of relevance for plasma physics is used as a testing ground for these problems.