Some numerical experiments using Newton's method for nonlinear parabolic and elliptic boundary-value problems

Authors:
Richard Bellman;Mario L. Juncosa;Robert Kalaba
Affiliations:
The RAND Corp., Santa Monica, CA;The RAND Corp., Santa Monica, CA;The RAND Corp., Santa Monica, CA
Venue:
Communications of the ACM
Year:
1961

Citing 0
Cited 2

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Journal of Computational and Applied Mathematics
A simple solution of the Bratu problem

Computers & Mathematics with Applications

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Abstract

Using a generalization of Newton's method, a non-linear parabolic equation of the form ut - uxx = g(u), and a non-linear elliptic equation uxx + uyy = eu, 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.