text: In the above equations () and (), we observe that the values required are at the faces, instead of the nodes. Hence approximations are required to fulfill this.
  In the central difference scheme we replace the value at the face with the average of the values at the adjacent nodes,
  :   and      ()
  By putting these values in equation () and rearranging we get the following result,
  where,
  In the Upwind scheme we replace the value at the face with the value at the adjacent upstream node. For example, for the flow to the right (Pe>0)as shown in the diagram, we replace the values as follows;
  : and     ()
  And for Pe < 0, we put the values as shown in the figure 3,
  : and   ()
  By putting these values in equation () and rearranging we get the same equation as equation (), with the following values of the coefficients: