Numerical Methods for Stochastic Partial Differential Equations with White Noise by Zhongqiang Zhang & George Em Karniadakis

Author:Zhongqiang Zhang & George Em Karniadakis
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

where , x i 1 = x i 2 = (i − 1)ℓ∕M s , i = 1, …, M s , and is the reference solution computed as explained above. The results demonstrating second-order convergence (see (6.1.11) and the discussion after Algorithm 6.1.4 ) are given in Table 6.7. Some control tests with δt = 1 × 10−5 and M = 1600 showed that the errors presented in this table are not essentially influenced by the errors caused by the choice of δt = 1 × 10−4 and cut-off of the basis at M = 900.  Table 6.7Performance of Algorithm 6.1.4 for passive scalar equation (6.4.4). The parameters of Algorithm 6.1.4 are N = 2, n = 1, M = 900, δt = 1 × 10−4.

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