*3.1. Forward Difference Scheme*

The forward difference scheme for heat Equation (2) is given by

$$w\_{n,j+1} = \alpha w\_{n+1,j} + (1 - 2\alpha)w\_{n,j} + \alpha w\_{n-1,j},$$

where *α* = *<sup>k</sup> <sup>h</sup>*<sup>2</sup> . Here *<sup>h</sup>* is the *<sup>x</sup>*−axis step size and *<sup>k</sup>* is the time step size for the grid points (*xi*, *tj*), where *xi* =*ih*, *tj* = *jk* for non-negative integers *i*, *j*. This scheme is Forward in Time and Centered in Space (FTCS). This method is explicit and converges to the solution for 0 <sup>&</sup>lt; *<sup>α</sup>* <sup>≤</sup> <sup>1</sup> <sup>2</sup> , so is conditionally stable [22].
