Time-Dependent Polynomial Chaos
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Abstract
Generalized polynomial chaos is known to fail for long-term integration, loosing its optimal convergence behavior and developing unacceptable error-levels. In this work, we present a time-dependent alternative of polynomial chaos in order to overcome these issues. This technique exists out of an on-the-fly reinitialization of the polynomial chaos expansion at different discrete time-levels. At those time-levels, the new polynomial chaos expansion will be created in terms of the stochastic solution. This time-dependent approach is applied on a stochastic ODE of which the results are compared with a standard gPC solution.
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