Evolution of Probability Distribution in Time for Solutions of Hyperbolic Equations
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- Evolution of Probability Distribution in Time for Solutions of Hyperbolic Equations
- Jung, Chang-Yeol
- Evolution of probability distribution; Monte Carlo integration; Monte Carlo simulation; Random interface; Random media; Stochastic partial differential equation
- Issue Date
- SPRINGER/PLENUM PUBLISHERS
- JOURNAL OF SCIENTIFIC COMPUTING, v.41, no.1, pp.13 - 48
- We investigate the evolution of the probability distribution function in time for some wave and Maxwell equations in random media for which the parameters, e.g. permeability, permittivity, fluctuate randomly in space; more precisely, two different media interface randomly in space. We numerically compute the probability distribution and density for output solutions. The underlying numerical and statistical techniques are the so-called polynomial chaos Galerkin projection, which has been extensively used for simulating partial differential equations with uncertainties, and the Monte Carlo simulations.
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