OICC Press Journal of Theoretical and Applied Physics 2251-7235 18 5 2024 10 30 A numerical solution for a nonlinear inverse stochastic parabolic problem based on Legendre wavelets bases 1 8 10.57647/j.jtap.2024.1805.62 EN Samaneh Parvaz Faculty of Mathematics, Khajeh Nasir Toosi University of Technology, Tehran, Iran https://orcid.org/0009-0008-3571-7948 Ali Zakeri Faculty of Mathematics, Khajeh Nasir Toosi University of Technology, Tehran, Iran https://orcid.org/0000-0002-6273-7855 Journal Article 2024 10 30 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 byemploying Legendre wavelets and their operational matrix. This method is combined with theLevenberg-Marquardt regularization technique. In continuation, the error analysis is given. Finally,a numerical sample confirms the efficiency and accuracy of this method.