A numerical solution for a nonlinear inverse stochastic parabolic problem based on Legendre wavelets bases

In this paper, we consider a 1D nonlinear stochastic partial differential equation of parabolic type. In this problem, values of the function on a part of physical boundary of the domain are unknown. A numerical approach has been developed to approximate the exact solution for this issue by employing Legendre wavelets and their operational matrix. This method is combined with the Levenberg-Marquardt regularization technique. In continuation, the error analysis is given. Finally, a numerical sample confirms the efficiency and accuracy of this method.