Numerical solution for stochastic heat equation with Neumann boundary conditions

In this article, we propose a new technique based on 2-D shifted Legendre poly?nomials through the operational matrix integration method to find numeri?cal solution of stochastic heat equation with Neumann boundary conditions. For proposed technique, convergence criteria and error estima?tion are also discussed in detail. This is tested two exam?ples, it observed that very easy handle such problems as initial conditions taken care automatically. Also, time complexity approach proved be O[k(N + 1)4] where N denotes degree approximate function k number simulations. convenient efficient for solving other partial differential equations.