Some Results in Two-Point Boundary Value Problems

Two new results in two-point boundary value problems are presented. The first is a modified method of adjoints which, under certain circumstances, will solve numerically two-point boundary value problems faster than the standard method of adjoints. The second result shows that Friedrichs' solution of the operator equation P(x) = 0 is really the modified Newton method. Kantorovich's sufficiency conditions for the convergence of the modified Newton's method are compared with Friedrichs' sufficiency conditions; it appears that, for most applications, the former conditions allow more leeway.