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