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