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Random coupled parabolic partial differential models are solved numerically using random cosine Fourier transform together with non‐Gaussian random numerical integration that captures the highly oscillatory behaviour of the involved integrands. Sufficient condition of spectral type imposed on the random matrices of the system is given so that the approximated stochastic process solution and its statistical moments are numerically convergent. Numerical experiments illustrate the results.

Integral transform solution of random coupled parabolic partial differential models