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

TL;DR

This paper explores stochastic solution methods for nonlinear PDEs with nonpolynomial and derivative terms, focusing on plasma physics equations to address challenges in constructing such solutions.

Contribution

It introduces approaches to handle nonpolynomial and derivative nonlinearities in stochastic PDE solutions, advancing numerical methods in plasma physics.

Findings

Effective stochastic solution strategies for complex nonlinear PDEs

Identification of challenges with nonpolynomial and derivative terms

Application to plasma physics equations demonstrates practical utility

Abstract

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.