Order of Crank-Nicolson scheme:

The Crank-Nicolson scheme to one-dimensional heat equation is given by

By applying Taylor series expansion for i-1, i+1 and n+1 terms we get

 

                                                                                                                             ................. (6.4.14)

since the left hand side of the equation is zero, the Crank Nicolson scheme is second order in space and also in time direction.