Question

advantage and disadvantage of lanrange formula

Answer 1

The obvious problem is that a higher order polynomial is huge. If I have 100 nodes then it will be a 99th degree polynomial. The values are unpredictable and will be wildly inaccurate between nodes. There is practically no advantage to using it other than it being intellectually simple.

For all practical purposes splines would be a better choice. Linear splines are extremely easy to calculate and have predictable behavior between nodes. Matlab uses them to plot. If you’re really particular you could also use quadratic splines for a piece wise function that is differentiable at the nodes.

Also, keep in mind that one of the key purposes of interpolation is creating a function for a solution to an ODE using a finite difference method. In this case, you may have 500–1000 nodes.