Extending the Usage of Newton’s Method with Applications to the Solution of Bratu’s Equation
Keyword(s):
We use Newton’s method to solve previously unsolved problems, expanding the applicability of the method. To achieve this, we used the idea of restricted domains which allows for tighter Lipschitz constants than previously seen, this in turn led to a tighter convergence analysis. The new developments were obtained using special cases of functions which had been used in earlier works. Numerical examples are used to illustrate the superiority of the new results.
2012 ◽
Vol 220-223
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pp. 2658-2661
Keyword(s):
2014 ◽
Vol 07
(01)
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pp. 1450007
2015 ◽
Vol 34
(2)
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pp. 197-211
2015 ◽
Vol 279
◽
pp. 318-335
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2019 ◽
Vol 17
(01)
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pp. 1843005
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