Review of iterative solutions to partial differential equations.

It may be useful to paste some material from here

Now pick an initial t, say $ t=0 $. Assume a boundary condition, $ x(0)=7 $.

Then $ x(0)=x_{0} $, so $ x_{0}=7 $.

Then $ x(\Delta t)=x_{1} $, so $ x_{1}=7+\Delta t2=7.2 $ (We pick $ \Delta t=0.2 $)

Then $ x(2\Delta t)=x_{2} $, so $ x_{2}=7.2+\Delta t2=7.4 $

[Plot of solution]