An implicit scheme, invented b John Crank (1916-) and Phyllis Nicolson (1917-1968), is based on numerical approximations for solutions at the point ![[Graphics:Images/CrankNicolsonMod_gr_68.gif]](http://www.ecs.fullerton.edu/%7Emathews/n2003/cranknicolson/CrankNicolsonMod/Images/CrankNicolsonMod_gr_68.gif)
that lies between the rows in the grid. Specifically, the approximation used for ![[Graphics:Images/CrankNicolsonMod_gr_69.gif]](http://www.ecs.fullerton.edu/%7Emathews/n2003/cranknicolson/CrankNicolsonMod/Images/CrankNicolsonMod_gr_69.gif)
is obtained from the central-difference formula,
![[Graphics:Images/CrankNicolsonMod_gr_70.gif]](http://www.ecs.fullerton.edu/%7Emathews/n2003/cranknicolson/CrankNicolsonMod/Images/CrankNicolsonMod_gr_70.gif)
.
that lies between the rows in the grid. Specifically, the approximation used for is obtained from the central-difference formula,. 
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