Quadrature Integration Techniques for Random Hyperbolic PDE Problems

[EN] 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 shownThis research has been funded by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017-89664-PCompany Rossi, R.; Egorova, VN.; Jódar Sánchez, LA. (2021). Quadrature Integration Techniques for Random Hyperbolic PDE Problems. Mathematics. 9(2):1-16. https://doi.org/10.3390/math90201601169