Triviality of a variable-timestep difference scheme for the heat equation (Q1974725)

The author considers the simplest difference scheme for the heat conduction equation \(\partial u/\partial t=\partial^2u/\partial x^2\) in the form of the explicit difference scheme \[ \frac{u_j^{n+1}- u_j^n}{\tau}= \frac{u_{j-1}^n- 2u_j^n+ u_{j+1}^n}{h^2} \] where \(u_j^n\) is the value of the grid function that approximates the solution to the heat equation at \((jh,n\tau)\). It is proved that the explicit difference scheme, given above, is actually a simple three-point explicit difference scheme with increased space step in the case of a one-dimensional heat conduction equation and a regular grid.