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0.45
0.4
0.35
0.3
0.25
u, v
0.2
0.15 2.2 A Finite Difference Approximation 49
0.1
0.05
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x
FIGURE 2.2. The figure shows the numerical solution (dashed line) and the exact
solution (solid line) of the boundary value problem. For the numerical scheme,
we have used n =5 interior grid points, and drawn a linear interpolation between
the values on the grid. The solution at the grid points are marked by ‘o’.

0.45
0.4
0.35
0.3
0.25
u, v
0.2
0.15
0.1
0.05
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x
FIGURE 2.3. The figure shows the numerical solution (dashed line) and the exact
solution (solid line) of the boundary value problem. For the numerical scheme,
we have used n =15 interior grid points.