SC²S Colloquium - August 26, 2015

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Date: August 26, 2015
Room: 02.07.023
Time: 3:00 pm, s.t.

Kathrin Retzer: Numerical Simulation of the Boundary Excited Atmospheric Heat Equation with the RPDE-RODE Reduction Method

Stochastic partial differential equations can be exceedingly difficult to solve. Thus, a new approach for boundary excited RPDEs who form a subset of SPDEs is presented and applied to a concrete parabolic RPDE, the atmospheric heat equation. RPDEs are hereby a simplified version of SPDEs where stochasticity is given in the time variable only, while in SPDEs stochasticity in space and time is quite common. In the given case a further simplification is made so that boundary excited RPDEs are examined, that means the stochasticity affects the main equation through the boundary condition only. To solve and simulate such an equation a vertical line approach is chosen. Hereby, the atmospheric heat equation is semidiscretised in space in order to obtain a large system of random ordinary differential equations. Then, already developed suited methods for RODEs can be applied to this large system.

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