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Statistical moments of the random linear transport equation. (English) Zbl 1211.65005

Summary: This paper deals with a numerical scheme to approximate the \(m\)th moment of the solution of the one-dimensional random linear transport equation. The initial condition is assumed to be a random function and the transport velocity is a random variable. The scheme is based on local Riemann problem solutions and Godunov’s method. We show that the scheme is stable and consistent with an advective-diffusive equation. Numerical examples are added to illustrate our approach.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R60 PDEs with randomness, stochastic partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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