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Extending the Usage of Newton’s Method with Applications to the Solution of Bratu’s Equation

by Ioannis K. Argyros 1,† and Daniel González 2,*,†
1
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
2
Escuela de Ciencias Físicas y Matemáticas, Universidad de Las Américas, Quito 170125, Ecuador
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2018, 6(12), 274; https://doi.org/10.3390/math6120274
Received: 15 October 2018 / Revised: 13 November 2018 / Accepted: 20 November 2018 / Published: 23 November 2018
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. View Full-Text
Keywords: Bratu; Newton; convergence Bratu; Newton; convergence
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Argyros, I.K.; González, D. Extending the Usage of Newton’s Method with Applications to the Solution of Bratu’s Equation. Mathematics 2018, 6, 274.

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