Solution of the Four Dimensional Fokker-Planck Equation: Still a Challenge
نویسنده
چکیده
The accurate prediction of the response of a dynamical system is a necessary first step toward its design and eventual control. Development of high fidelity models of the system and excitation processes provides the means to accurately determine system response, assess the adequacy of the system in terms of its performance and safety, and suggest remedial action. However, a degree of uncertainty exists in the properties of nearly every physical system, as well as in most excitations. Thus, the predicted responses, at some scale, will contain some randomness, and the complete and accurate determination of these responses is a nontrivial matter. Here, we discuss the problems inherent in the analysis of a particular class of systems using the finite element method to solve related Fokker-Planck equations.
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