An approximate solution for stochastic Burgers' equation driven by white noise

This paper proposes an approximate solution based on two-dimensional shifted Legendre polynomials, together with its operational matrices of integration and stochastic integration for solving stochastic Burgers' equations with a space-uniform white noise and with variable coefficients. The aforementioned operational matrices transform the problem under consideration into a system of algebraic equations. The error analysis in the L-2 norm for the proposed method is discussed in detail. The transformation is done by taking into account the initial and boundary conditions. Hence, the proposed method is very simple for solving such problems. Numerical examples discussed confirm the efficiency and accuracy of the proposed method. A simulation study was carried out. An algorithm was developed and implemented on Maple software.