A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere
This work provides a numerical method for solving stochastic PDEs on spheres, which is relevant for geophysical modeling but represents an incremental improvement over existing spectral and Euler methods.
The paper develops a non-uniform temporal discretization for stochastic heat equations on the sphere, demonstrating its effectiveness through numerical experiments inspired by NASA's Earth surface temperature data.
We investigate a discretization of a class of stochastic heat equations on the unit sphere with multiplicative noises. A spectral method is used for the spatial discretization and the truncation of the Wiener process, while an implicit Euler scheme with non-uniform steps is used for the temporal discretization. Some numerical experiments inspired by Earth's surface temperature data analysis GISTEMP provided by NASA are given.