By James L. Blue
Communications of the ACM,
June 1969,
Vol. 12 No. 6, Pages 327-330
10.1145/363011.363151
Comments
The solution of the nonlinear differential equation Y″ = F(x, Y, Y′) with two-point boundary conditions is approximated by a quintic or cubic spline function y(x). The method is well suited to nonuniform mesh size and dynamic mesh size allocation. For uniform mesh size h, the error in the quintic spline y(x) is O(h4), with typical error one-third that from Numerov's method. Requiring the differential equation to be satisfied at the mesh points results in a set of difference equations, which are block tridiagonal and so are easily solved by relaxation or other standard methods.
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