A new explicit three-level difference scheme for the solution of the heat flow equation

A new explicit three-level difference scheme for the numerical solution of the heat flow equation is proposed. The main features of the new scheme are: i) it is unconditionally stable, ii) it is very highly accurate from the point of view of the truncation error, and iii) its solution converges to the solution of the heat equation even if the time and the distance increments tend to zero independently.