Spline Function Methods for Nonlinear Boundary-Value Problems

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(h^4), 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.

CACM June, 1969

Blue, J. L.

boundary value problems, differential equations,
finite differences, functional approximation, 
iterative methods, nonlinear equations, spline functions

5.13 5.15 5.17

CA690605 JB February 17, 1978  11:07 AM

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