Some Numerical Experiments Using Newton's Method for Nonlinear Parabolic and EllipticBoundary-Value Problems Using a generalization of Newton's method, a nonlinear parabolic equation of the form U(t)-U(xx)=g(U) and a nonlinear elliptic equation U(xx)+U(yy)=exp(U) are solved numerically Comparison of these results with results obtained using the Picard iteration procedure show that in many cases the quisi linearization method offers substantial advantages in both time and accuracy. CACM April, 1961 Bellman, R. Juncosa, M. L. Kalaba, R. CA610433 JB March 16, 1978 11:20 PM 335 5 335 335 5 335 335 5 335