Preprint MA 61/2007

On the Worst Scenario Method: A Modified Convergence Theorem and Its Application to an Uncertain Differential Equation

Petr Harasim

We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in the literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient.