Integral Transform Solution of Random Coupled Parabolic Partial Differential Models

TL;DR

This paper introduces a numerical method combining random cosine Fourier transform and non-Gaussian integration to solve random coupled parabolic PDEs, ensuring convergence of solutions and moments.

Contribution

It presents a novel numerical approach for solving stochastic coupled PDEs with convergence guarantees under spectral conditions.

Findings

Method accurately captures oscillatory behavior.

Numerical experiments confirm convergence.

Approach applicable to complex stochastic PDEs.

Abstract

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