@Carl Love for the value of X=0.5 and tau=0.8 and i want to plot eta versus tau for different values of Nr  tau range is 0..2  efficiency_plots.pdf this is the demo figure for the reference here eta is efficiency 

modifed_practice.mw  

waiting for the reply sir 

Thank you

@tomleslie 

I need to plot by using the equations 11,12,13 and 14  from both i need same graphs 

U plotted by using the equations 7,8,9 and 10.

  @tomleslie How to remove error both numeric and Hpm solutions should be nearly same

@tomleslie  sir this is not FDM method 

This is normal dsolve method.

But I m asking about Crank nicolson method 

In that  all terms are mentioned uij uij+1...

With boundary conditions