Interpolation, approximation and differential equations solvers

Solving ordinary differential equations I: Nonstiff problems, second edition.J. C. Butcher, Numerical methods for ordinary differential equations, ISBN 0471967580.Unlike interpolation, it does not require the fitted function to intersect each point.So, we see that polynomial interpolation solves all the problems of linear interpolation.However, polynomial interpolation also has some disadvantages.Furthermore, polynomial interpolation may not be so exact after all, especially at the end points.These disadvantages can be avoided by using spline interpolation.Table 1. Results of interpolation by different methods in the given points.Table 2. Table of Average deviation between average deviation and interpolation results.Method of least squares interpolation.