Some Numerical Results for Iterative Continuation in Nonlinear Boundary-value Problems

In this communication we apply certain continuous analog iterative methods to two sample boundary-value problems. We show that the Euler-Newton and the second-order continuation of the Newton method are both useful algorithms for obtaining solutions to classes of nonlinear boundary-value problems. For a convergence analysis we rely upon a number of convergence theorems presented in earlier work. We indicate, through the numerical results, that the relaxed Newton methods are particularly useful in the iterative solution of “strongly” nonlinear problems where little information is available concerning “good starting values.”