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 Schr\"odinger equation on the unit sphere.

翻译：光谱方法接近于单元球体上蒸汽波方程式的解决方案。 提供了强、弱、几乎可以肯定的拟议数字方法的趋同率,并显示仅仅取决于驱动噪音的平滑和初始条件。 数字实验证实了理论率。 开发的数字方法扩展至较高维域的蒸汽波方程式和单位域的免费蒸汽 Schr\'odinger方程式。