Extending the Mesh Independence For Solving Nonlinear Equations Using Restricted Domains
| Autor: | Rami M. Younis, Ioannis K. Argyros, Santhosh George, Á. Alberto Magreñán, Soham M. Sheth |
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| Rok vydání: | 2017 |
| Předmět: |
Discretization
Applied Mathematics Banach space 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Algebra Independence principle Computational Mathematics Nonlinear system symbols.namesake symbols Computational Science and Engineering Independence (mathematical logic) 0101 mathematics Newton's method Mathematics |
| Zdroj: | International Journal of Applied and Computational Mathematics. 3:1035-1046 |
| ISSN: | 2199-5796 2349-5103 |
| DOI: | 10.1007/s40819-017-0398-1 |
| Popis: | The mesh independence principle states that, if Newton’s method is used to solve an equation on Banach spaces as well as finite dimensional discretizations of that equation, then the behaviour of the discretized process is essentially the same as that of the initial method. This principle was inagurated in Allgower et al. (SIAM J Numer Anal 23(1):160–169, 1986). Using our new Newton–Kantorovich-like theorem and under the same information we show how to extend the applicability of this principle in cases not possible before. The results can be used to provide more efficient programming methods. |
| Databáze: | OpenAIRE |
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