Numerical approximation and simulation of the stochastic wave equation on the sphere
Preprint, 2021

Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods.Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of the driving noise and the initial conditions. Numerical experiments confirm the theoretical rates.The developed numerical method is extended to stochastic wave equations on higher-dimensional spheres and to the free stochastic Schrödinger equation on the unit sphere.

Author

David Cohen

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Numerical analysis and simulation of PDEs with random dispersion

Swedish Research Council (VR), 2019-01-01 -- 2022-12-31.

Efficient approximation methods for random fields on manifolds

Swedish Research Council (VR), 2021-01-01 -- 2024-12-31.

Subject Categories

Computational Mathematics

Mathematical Analysis

Related datasets

URI: https://arxiv.org/abs/2102.04224

More information

Created

2/9/2021 6