Approximation: Linear interpolation

We modify the result of gird method in the following way:

where red points are the results from grid method.

There is no change on the gird. We linearly interpolate two adjacent points.

As a result, we get points as they look on the graph.

If the adjacent two points are (k1,k1’) and (k2,k2’), we can interpolate

linearly for (k0,k0’). If k0=k1 or k0=k2, k0’=k1’ or k0’=k2’ itself.