Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations

摘要

This paper deals with the error analysis of generalized polynomial chaos (gPC) for nonlinear random ordinary differential equations. The analysis shows that the global error mainly relies on the projection error and the numerical error. For the deterministic systems obtained from the gPC method, a kind of numerical approach with error analysis is given. At last, a numerical experiment is carried out to support the theoretical results.