In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

中文翻译：

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随机双曲PDE问题的正交积分技术

在本文中，我们考虑遵循均方方法和Laplace变换技术的随机双曲型偏微分方程（PDE）问题。随机性不仅需要近似随机过程的计算，还需要其统计矩。因此，适当的数值方法应该允许期望和方差的有效计算。在这里，我们使用几种积分技术，包括中点正交法则，高斯-拉格勒正交及其扩展以及Talbot算法，分析了围绕拉普拉斯逆变换及其评估的不同数值方法。显示了仿真，数值收敛和带有实验的计算过程时间。