An approximate Solution of Heat Equation in Three Dimensions by LOD Method

In this paper, we solve one of the parabolic partial differential equations in three dimensions which is heat equation with Locally One Dimension methods, and by comparing the results by this method with the exact solution, we see that the results are nearest to the solution and specially of the implicit method (Crank-Nicholson). Then we study the numerical stability, numerical consistency and numerical convergence of these methods which shows that its unconditionally stable with (C-N) and conditionally stable with explicit scheme. Consistence and converge are realized.