A spectral collocation approach is constructed to solve a class of time-fractional stochastic heat equations (TFSHEs) driven by Brownian motion. Stochastic differential equations with additive noise have an important role in explaining some symmetry phenomena such as symmetry breaking in molecular vibrations. Finding the exact solution of such equations is difficult in many cases. Thus, a collocation method based on sixth-kind Chebyshev polynomials (SKCPs) is introduced to assess their numerical solutions. This collocation approach reduces the considered problem to a system of linear algebraic equations. The convergence and error analysis of the suggested scheme are investigated. In the end, numerical results and the order of convergence are evaluated for some numerical test problems to illustrate the efficiency and robustness of the presented method.

中文翻译：

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求解加性噪声驱动的时间分数随机热方程的一种搭配方法

构建了一种光谱搭配方法来求解一类由布朗运动驱动的时间分数随机热方程 (TFSHE)。具有加性噪声的随机微分方程在解释分子振动中的对称性破缺等一些对称现象方面具有重要作用。在许多情况下，找到此类方程的精确解是很困难的。因此，引入了一种基于第六类切比雪夫多项式 (SKCP) 的搭配方法来评估它们的数值解。这种搭配方法将所考虑的问题简化为线性代数方程组。研究了所建议方案的收敛性和误差分析。到底，