Cubic spline solutions of boundary value problems over infinite intervals

摘要

A cubic spline method for the numerical solution of a two-point boundary value problem posed on an infinite interval involving a second order linear differential equation is described. By reducing the infinite interval to a finite interval which is large and imposing appropriate asymptotic boundary condition at the far end, the resulting boundary value problem is treated by using the cubic spline approximation. The tridiagonal system resulting from the spline approximation is efficiently solved by the method of sweeps. The stability of the method is analysed and the theory is illustrated by solving test examples.