Cubic Spline Interpolation

Function: - Cubic Spline Interpolation 4

When using this function we need to be very careful. If x is close to zero the function ln(x) is going to be infinity. Therefore the function sin(ln(x)) will have a high speed change (first derivative ) value from -1 to 1. As the function moves to zero the number of oscillations will be increased. If we use too small a node number it will result in the interpolation missing some of the maximums and minimums.

Graph 7. Showing function close to zero. What is interesting is the function shape from 0.58 to 3.91 compared to the next interval 3.91 to 10.44. This is because at 0.58 the curve is expected to reach an amplitude of 1 but as it is the edge of the interval and there are not enough nodes to reach 1. The next Graph 8. will show more details.

Graph 8. Showing function which is much closer to zero compared to Graph 7.

Using a small number of nodes will result in missing one whole oscillation (purple line) compared to the Cubic Spline interpolation (blue line). After 0.10 the function interpolation is very good.