SOME NUMERICAL EXPERIMENTS USING NEWTON'S METHOD FOR NONLINEAR PARABOLIC AND ELLIPTIC BOUNDARY-VALUE PROBLEMS
RAND CORP SANTA MONICA CA
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Using a generalization of Newtons method, a nonlinear parabolic equation of the form u sub t - u sub xx gu, and a nonlinear elliptic equation u sub xx u sub yy e superscript 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.
- Theoretical Mathematics