Affiliation:
1. The RAND Corp., Santa Monica, CA
Abstract
Using a generalization of Newton's method, a non-linear parabolic equation of the form
u
t
-
u
xx
=
g
(
u
), and a non-linear elliptic equation
u
xx
+
u
yy
=
e
u
, are solved numerically. Comparison of these results with results obtained using the Picard iteration procedure show that in many cases the quasilinearization method offers substantial advantages in both time and accuracy.
Publisher
Association for Computing Machinery (ACM)
Reference12 articles.
1. HESTENES M. R. Numerical methods of obtaining solutions of fixed end point problems in the calculus of variations. The RAND Corporation Research Memorandum RM-102 14 August 1949. HESTENES M. R. Numerical methods of obtaining solutions of fixed end point problems in the calculus of variations. The RAND Corporation Research Memorandum RM-102 14 August 1949.
2. On methods for obtaining solutions of fixed end-point problems in the calculus of variations
3. Functional analysis and applied mathematics;KANTOROVICH L. V;Uspekhi Matem. Nauk,1948
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