SKEDSOFT

Numerical Methods

or

.............................1.8

This relation gives a system of n – 1 linear equations in n 1 unknowns M0, M1, ..., Mn. The two additional conditions required are the natural spline conditions M0 = 0 = Mn. These equations are solved for M1, M2, ..., Mn-1. Substituting these values in (1.4), we obtain the spline valid in the interval [xi-1, xi]. If the derivative is required, we can find it from (1.6). Equispaced data When the data is equispaced, we have hi = hi 1 = h and xi = x0 ih. Then, the spline in the interval [xi-1, xi], given in (1.4) and the relation between the second derivatives given in (1.8) simplify as

..................................1.9

...............................2.0