Checking Finite Difference Errors

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 and .
By using DSolve and RSolve, a numerical solution is completely avoided.

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