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The semi‐analytical method for time‐dependent wave problems with uncertainties
Author(s) -
Bartual Maria Consuelo Casabán,
López Juan Carlos Cortés,
Sánchez Lucas Jódar
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5813
Subject(s) - mathematics , hermite polynomials , quadrature (astronomy) , gaussian quadrature , constructive , fourier transform , gauss , computation , representation (politics) , mathematical analysis , nyström method , algorithm , process (computing) , integral equation , physics , electrical engineering , quantum mechanics , politics , computer science , law , political science , engineering , operating system
This paper provides a constructive procedure for the computation of approximate solutions of random time‐dependent hyperbolic mean square partial differential problems. Based on the theoretical representation of the solution as an infinite random improper integral, obtained via the random Fourier transform method, a double approximation process is implemented. Firstly, a random Gauss‐Hermite quadrature is applied, and then, the evaluations at the nodes of the integrand are approximated by using a random Störmer numerical method. Numerical results are illustrated with examples.