The exact solution of the boundary value problem
,
at
, and
at
with parameter
is
.
The second-order discretization for the discrete variable
at points
with step size
gives the recurrence equation
, where
,
, which is solved exactly using
Mathematica's
RSolve function.
The difference between the finite difference and exact solutions in the region
is dynamically plotted in the solution region
for 3 to 300 discretization points and parameter
between -10 and 10.
By using
DSolve and
RSolve, a numerical solution is completely avoided.
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