Implicit method of high accuracy on hexagonal grids for approximating the solution to heat equation on rectangle

A two layer Implicit method on hexagonal grids is proposed for approximating the solution to first type boundary value problem of heat equation on rectangle. It is proven that the given implicit scheme is unconditionally stable and converges to the exact solution on the grids of order O(h4+τ2) where, h and 32h are the step sizes in space variables x1 and x2 respectively and τ is the step size in time. The method is applied on a test results.