Interpolation of Unequally Spaced Points

These methods are based on the concept of interpolation of unequally spaced points that is, choosing a function, usually a polynomial, that approximates the solution of a differential equation in the range of integration, Xq x < and determining the coefficients of that function from a set of base points. 

Finite difference methods, and interpolation of equally and unequally spaced points... 

Another method of integrating unequally spaced data points is to interpolate the data using a suitable interpolation method, such as cubic splines, and then evaluate the integral from the relevant polynomial. Therefore, the integral of Eq. (4.66) may be calculated by integrating Eq. (3.143) over the interval jcJ and summing up these terms for all the intervals ... 

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