Here is some code I wrote for the Heat equation in 1D
The blog post ran with the following parameters:
time seq 0 199 | xargs -I{} -P 7 ./heat_1d.x {} 9 1000000 .1 .01 1. >/dev/null
heat_inplace_1d.c does the same as heat_1d.c but with inplace FFTs (see FFTW documentation)
heat_jentzen_1d.c applies the algorithm of:
Arnulf Jentzen, Peter Kloeden, and Georg Winkel. "Efficient simulation of nonlinear parabolic SPDEs with additive noise." The Annals of Applied Probability 21.3 (2011): 908-950.
The simulation of the Ornstein-Uhlenbeck equation with an exact algorithm is shown in the ornstein-uhlenbeck.ipynb file. This is applied to the Heat equation (and to nonlinear equations) in the Jentzen-Kloeden-Winkel algorithm. The random variables must be normal random variables in this case. In the predictor-corrector algorithm, I used a uniform random variable with unit variance.
RNG for standard normal random variables was slightly modified at p=0 and p=1, use a different algorithm for serious applications